Find all values of x for which the series converges. For these values of x, write the sum of the series as a function of x. sum_{n=1}^infty(3x)^n

beljuA

beljuA

Answered question

2021-02-25

Find all values of x for which the series converges. For these values of x, write the sum of the series as a function of x.
n=1(3x)n

Answer & Explanation

tabuordg

tabuordg

Skilled2021-02-26Added 99 answers

Consider the series
n=1(3x)n
Consider a G.P series n=1rn
Series is convergent for |r|<1
Sum of this infinite series is given by
S=a1r
n=1(3x)n=(3x)1+(3x)2+(3x)3+(3x)4....
n=1(3x)n=(3x)+(3x)2+(3x)3+(3x)4....
The given series is a Geometric progression with the
first term =3x
common ratio =3x
The given series is convergent for

|3x|<1

1<3x<1

13

Sum of the series

n=1(3x)n

for 13

Here

a=3x,r=3x

S=a1r

S=3x13x

Answer:

Series is convergent for 13

Sum of the series is 3x13x

Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-27Added 2605 answers

Answer is given below (on video)

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