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

x belongs to (-8,-6)

Step-by-step explanation:

Given is a series in x as

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

An infinite geometric series converges only for

|r|<1

Hence here we have if series converges,

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

table 3 represents a direct variation function. : )