Compute the following sum of a geometric sequence: S = 0.936 + 0.935 + ... + 0.92 + 0.9 + 1 (Round your answer to two decimal pl

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mezya [45] · Answer 1 · 2022-09-06T03:59:32+03:00

The sum of the given geometric sequence to 2 dp is 936.00

To get the sum of a geometric sequence, we will use the formula for calculating the sum to infinity of the sequence as shown:

$S_\infty=\frac{1}{1-r}$

a is the first term

r is the common ratio

Given the sequence S = 0.936 + 0.935 + ... + 0.92 + 0.9 + 1

a = 0.936

r = 0.935/0.936 = 0.998

Substitute into the formula

$S_\infty=\frac{0.936}{1-0.999}\\S_\infty=\frac{0.936}{0.001}\\S_\infty=936$

Hence the sum of the given geometric sequence to 2 dp is 936.00