Video:Rules for determining interval of convergence

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Rules for determining interval of convergence (6 videos)

Statement

(see first video below)

Explanation

(see first video below)

Hierarchy of functions

List of functions

(see first video below)

Interaction between functions

(see first video below)

Remember that all these are functions in $k$

(see first video below)

Determination of interval of convergence

Superexponential growth and decay

Subexponential growth and decay: degree difference test

Subexponential growth and decay: degree difference test with cautionary use where exponent is a multiple of the index of summation

Subexponential growth and decay: examples where the exponent is a power of the index of summation

(see video above)

Video:Rules for determining interval of convergence

Statement

Explanation

Hierarchy of functions

List of functions

Interaction between functions

Remember that all these are functions in $k$

Determination of interval of convergence

Superexponential growth and decay

Subexponential growth and decay: degree difference test

Subexponential growth and decay: degree difference test with cautionary use where exponent is a multiple of the index of summation

Subexponential growth and decay: examples where the exponent is a power of the index of summation

Exponential growth or decay: degree difference test on coefficients

Exponential growth or decay: cautionary use where the exponent is a multiple of the summation index

Tricky examples

Statement

Explanation

Hierarchy of functions

List of functions

Interaction between functions

Remember that all these are functions in k {\displaystyle k}

Determination of interval of convergence

Superexponential growth and decay

Subexponential growth and decay: degree difference test

Subexponential growth and decay: degree difference test with cautionary use where exponent is a multiple of the index of summation

Subexponential growth and decay: examples where the exponent is a power of the index of summation

Exponential growth or decay: degree difference test on coefficients

Exponential growth or decay: cautionary use where the exponent is a multiple of the summation index

Tricky examples

Remember that all these are functions in $k$