Can anyone help me with the answer for number 4
1 answer:
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The series converges to 1/(1-9x) for -1/9<x<1/9
Given the series is ∑
We have to find the values of x for which the series converges.
We know,
∑ converges to (a) / (1-r) if r < 1
Otherwise the series will diverge.
Here, ∑ is a geometric series with |r| = | 9x |
And it converges for |9x| < 1
Hence, the given series gets converge for -1/9<x<1/9
And geometric series converges to a/(1-r)
Here, a = 1 and r = 9x
Therefore, a/(1-r) = 1/(1-9x)
Hence, the given series converges to 1/1-9x for -1/9<x<1/9
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we are given
geometric sequence -36, 6, -1, 1/6, ...
first term is -36
now, we can find common ratio
now, we can find nth term
now, we can plug values
and we get
now, we can find 5th term , 6th term, 7th term
fifth term:
sixth term:
seventh term:
so, next terms are
,
, .............Answer