Question

Does the sequence 100, 90, 81, 72.9,….. converge or diverge and why?

Answer 1

From the series given below

100, 90, 81, 72.9

You noticed you were right when you said the common ratio r = 0.9

Suh a series oconverges. This is because the common ratio r is less than 1.

So when a series has r < 1, as seen in this type, it is said that such as series converges. And hence we ca find the sum to infinity of such series given as

`\begin{gathered} S=(a)/(1-r) \\ Where\text{ S is the sum to infinity, a the first term and r the common ratio } \end{gathered}`