Find the values of x for which the series converges. (Enter your answer using interval notation.) [infinity] (x + 7)n n = 1

Question

Find the values of x for which the series converges. (Enter your answer using interval notation.) [infinity] (x + 7)n n = 1

in progress 0
Adeline 2 days 2021-10-12T07:01:22+00:00 1 Answer 0

Answers ( )

    0
    2021-10-12T07:02:37+00:00

    Answer:

    x belongs to (-8,-6)

    Step-by-step explanation:

    Given is a series in x as

    \Sigma _1^{\infty} (x+7)^n\\=(x+7)+(x+7)^2+(x+7)^3+(x+7)^4+(x+7)^5+...(x+7)^n+...

    we find that first term is x+7 and each successive term is multiplied by x+7

    In other words this is a geometric series with common ratio as

    r=x+7\\a=x+7

    An infinite geometric series converges only for

    |r|<1

    Hence here we have if series converges,

    |x+7|<1\\-1<x+7<1\\-8<x<-6

    For all values of x lying in the open interval (-8,-6) the series converges.

Leave an answer

Browse
Browse

27:3+15-4x7+3-1=? ( )