## Power series expansions

Power series expansions $$ 1. \ e^x = 1+x+ \frac {x^2}{2!} + \frac {x^3}{3!} + \cdots + \frac {x^n}{n!}+ \cdots $$ $$ 2. \ a^x=1+ \frac {x \ln a}{1!}+ \frac…

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# Arithmetic Series formulas

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Power series expansions

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Binomial series

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Finite series

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Geometric series

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Arithmetic Series

Power series expansions $$ 1. \ e^x = 1+x+ \frac {x^2}{2!} + \frac {x^3}{3!} + \cdots + \frac {x^n}{n!}+ \cdots $$ $$ 2. \ a^x=1+ \frac {x \ln a}{1!}+ \frac…

Binomial series $$ 1. \ \frac {1}{1+x} = 1-x+x^2-x^3+\cdots, \ |x| \lt 1 $$ $$ 2. \ \frac {1}{1-x} = 1+x+x^2+x^3+\cdots, \ |x| \lt 1 $$ $$ 3. \ \sqrt…

Finite series A finite series is a summation of a finite number of terms. Sum of first n natural numbers: $$ 1+ 2+ 3+\cdots = \frac {n(n+1)}{2} $$ Example: Find…

Geometric series A geometric series is a series whose related sequence is geometric. It results from adding the terms of a geometric sequence In General we write a Geometric Sequence…

Arithmetic Series An arithmetic series is the sum of the terms in an arithmetic sequence with a definite number of terms. In General we could write an arithmetic sequence like…