Sequences, Series, Exponential Functions, and Logarithmic Functions - Class 11 Formulas, Worksheets, and Examples

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Mira

5/28/2023

Algebra 2

sequences, series, exponential functions, the number e, and logarithmic functions

Subjects

Algebra 2

Geometric Series

Sequences, Series, Exponential Functions, and Logarithmic Functions - Class 11 Formulas, Worksheets, and Examples

Name: Knowunity
Brand: Knowunity

A comprehensive guide to sequences and series class 11 and related mathematical concepts, focusing on fundamental principles, formulas, and practical applications.

• The guide covers essential topics including sequences and series formulas, exponential functions, logarithms, and their properties
• Detailed explanations of arithmetic and geometric series, including partial sums and convergence conditions
• In-depth coverage of exponential functions and the number e, including real-world applications
• Comprehensive overview of logarithmic functions and properties, including graphing techniques and solving equations
• Practical examples and problem-solving strategies throughout the material

...

5/28/2023

980

<p>The study guide for Class 11 Sequences and Series covers the definition and notation of sequences, as well as various types of sequences

View

Page 2: Series and Summation Notation

This page delves into series calculations and sigma notation, providing fundamental properties and special series formulas.

Definition: A series is the sum of terms in a sequence, represented using sigma notation $Σ$ .

Vocabulary: Sigma notation includes:

Index of summation $x$
Lower bound $starting term$
Upper bound $last term$

Example: The sum of constants: Σc from x=1 to n equals c·n

Highlight: Key summation properties include:

Sum of functions: Σ $f(x) + g(x)$ = Σf $x$ + Σg $x$
Constant multiplication: Σcf $x$ = cΣf $x$

View

Page 3: Advanced Series and Exponential Functions

This section covers arithmetic and geometric series, introducing exponential functions and their properties.

Definition: Exponential functions are those where the dependent variable increases/decreases by a constant multiple.

Example: Basic exponential function: y = a $b$ ˣ

Highlight: For exponential functions:

Domain is $-∞,∞$
Range depends on 'a': $k,∞$ if a>0; $-∞,k$ if a<0

Vocabulary: In exponential functions:

b is the base/common ratio
a is the initial/critical value
h is horizontal shift
k is vertical shift

View

Page 4: The Number e and Logarithms

This final section introduces the number e and logarithmic functions, connecting them to real-world applications.

Definition: e is an irrational number $≈2.718$ serving as the natural base for logarithms.

Example: Compound interest formula: A = P $1 + r/n$ ⁿ

Highlight: Logarithmic functions are inverses of exponential functions, used when solving for variables in exponents.

Quote: "Logarithmic functions are the inverses of exponential functions"

Vocabulary: In compound interest:

A is account balance/future value
P is principal/initial deposit
r is annual interest rate
t is time in years
n is compounding frequency

View

Page 4: Exponential Functions and e

This section explores exponential functions and the number e pdf content, including practical applications.

Definition: The number e is an irrational number approximately equal to 2.718, often called Euler's number.

Example: Compound interest formula: A = P $1 + r/n$ ^ $nt$

Highlight: The function y = e^x represents exponential growth with domain $-∞,∞$ and range $0,∞$ .

View

Page 5: Logarithmic Functions

This page details logarithmic functions and properties worksheet concepts, focusing on graphing and transformations.

Definition: The general form of a logarithmic function is f $x$ = alog_b $x-h$ + k

Highlight: Key characteristics include:

Vertical asymptote at x = h
Domain: $h,∞$
Range: $-∞,∞$

View

Page 6: Properties of Logarithms

This section covers essential properties of logarithms examples and fundamental concepts.

Definition: Key logarithmic properties include base cancellation and product rules.

Example: log_2 $2^3$ = 3 $when bases are equal, the logarithm equals the exponent$

Highlight: The product rule states that log_a $MN$ = log_a $M$ + log_a $N$

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Subjects

Algebra 2

Geometric Series

Algebra 2

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980

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Jul 3, 2025

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7 pages

Sequences, Series, Exponential Functions, and Logarithmic Functions - Class 11 Formulas, Worksheets, and Examples

Mira

@miraa._noui

A comprehensive guide to sequences and series class 11 and related mathematical concepts, focusing on fundamental principles, formulas, and practical applications.

• The guide covers essential topics including sequences and series formulas, exponential functions, logarithms, and their properties
•... Show more

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Page 2: Series and Summation Notation

This page delves into series calculations and sigma notation, providing fundamental properties and special series formulas.

Definition: A series is the sum of terms in a sequence, represented using sigma notation $Σ$ .

Vocabulary: Sigma notation includes:

Index of summation $x$
Lower bound $starting term$
Upper bound $last term$

Example: The sum of constants: Σc from x=1 to n equals c·n

Highlight: Key summation properties include:

Sum of functions: Σ $f(x) + g(x)$ = Σf $x$ + Σg $x$
Constant multiplication: Σcf $x$ = cΣf $x$

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Page 3: Advanced Series and Exponential Functions

This section covers arithmetic and geometric series, introducing exponential functions and their properties.

Definition: Exponential functions are those where the dependent variable increases/decreases by a constant multiple.

Example: Basic exponential function: y = a $b$ ˣ

Highlight: For exponential functions:

Domain is $-∞,∞$
Range depends on 'a': $k,∞$ if a>0; $-∞,k$ if a<0

Vocabulary: In exponential functions:

b is the base/common ratio
a is the initial/critical value
h is horizontal shift
k is vertical shift

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Page 4: The Number e and Logarithms

This final section introduces the number e and logarithmic functions, connecting them to real-world applications.

Definition: e is an irrational number $≈2.718$ serving as the natural base for logarithms.

Example: Compound interest formula: A = P $1 + r/n$ ⁿ

Highlight: Logarithmic functions are inverses of exponential functions, used when solving for variables in exponents.

Quote: "Logarithmic functions are the inverses of exponential functions"

Vocabulary: In compound interest:

A is account balance/future value
P is principal/initial deposit
r is annual interest rate
t is time in years
n is compounding frequency

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Page 4: Exponential Functions and e

This section explores exponential functions and the number e pdf content, including practical applications.

Definition: The number e is an irrational number approximately equal to 2.718, often called Euler's number.

Example: Compound interest formula: A = P $1 + r/n$ ^ $nt$

Highlight: The function y = e^x represents exponential growth with domain $-∞,∞$ and range $0,∞$ .

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Page 5: Logarithmic Functions

This page details logarithmic functions and properties worksheet concepts, focusing on graphing and transformations.

Definition: The general form of a logarithmic function is f $x$ = alog_b $x-h$ + k

Highlight: Key characteristics include:

Vertical asymptote at x = h
Domain: $h,∞$
Range: $-∞,∞$

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Page 6: Properties of Logarithms

This section covers essential properties of logarithms examples and fundamental concepts.

Definition: Key logarithmic properties include base cancellation and product rules.

Example: log_2 $2^3$ = 3 $when bases are equal, the logarithm equals the exponent$

Highlight: The product rule states that log_a $MN$ = log_a $M$ + log_a $N$

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Page 1: Fundamentals of Sequences

This page introduces the core concepts of sequences and their mathematical representation. The content focuses on both arithmetic and geometric sequences, providing essential formulas and notations.

Definition: A sequence is an ordered list of objects or numbers, with each item denoted as a "term".

Vocabulary: Domain of a sequence refers to consecutive list of terms $1, 2, 3, 4...n$ , while range represents the actual values in the sequence.

Example: For an arithmetic sequence 1, 3, 5, 7, the range is {1, 3, 5, 7}.

Highlight: Two key types of sequences are introduced:

Arithmetic sequences with constant difference $d$
Geometric sequences with constant ratio $r$

Quote: "The rule for arithmetic sequence: an = a₁ + d $n-1$ OR an = an-1 + d"

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