Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. (If the quantity diverges,

Question

2 years ago

5

enter DIVERGES.) 9 + 8 + 64 9 + 512 81 +

1 answer:

pogonyaev · Answer 1 · 2023-12-08T04:44:58+03:00

The given geometric series is convergent and the sum of this series is 81.

According to the statement

we have given that the geometric series and we have to find that the convergent or divergent and If it is convergent, find its sum.

So, For this purpose, we know that the

The given geometric series is

9 + 8 + 64/9 + 512/81 + .....

And the common ratio from this G.P. series

r = term 2 / term 1 = 8/9

So, r = 8/9

8/9 < 1

so This series is convergent.

And now the sum of series is according to the summation formula:

Sum = 9/(1 - 8/9)

Sum = 9/(1/9)

Sum = 81.

So, The given geometric series is convergent and the sum of this series is 81.

Learn more about Geometric series here

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