Report error find the sum of the series 1 + \frac{1}{2} + \frac{1}{10} + \frac{1}{20} + \frac{1}{100} + \cdots, where we alternately multiply by \frac 12 and \frac 15 to get successive terms.

The sum of given  series is 5/3.

Step-by-step explanation:

Given series is

We need to find the sum of above series. In this series we alternately multiply by  1/2 and 1/5 to get successive terms.

Isolate the odd and even place terms.

Now, we have two infinite series.

Sum of an infinite GP is

where, r is first term and r is common ratio, 0 < r < 1.

In

First term = 1

Common ratio = 1/10

In

First term = 1/2

Common ratio = 1/10

The sum of given series is

Therefore the sum of given  series is 5/3.

i use my brain for prombles like this maybe you could try it

step-by-step explanation: