Question

The sum of infinite series 1/5-2/25+4/75-8/625.... ?​

Answer 1

1/7

Explanation:

Given series :-

• 1/5 -2/25 +4/125 - 8/625 ( correct)

To find :-

• The sum of infínite Series .

From the Series , the common ratio will be ,

⇝ CR = -2/25 ÷ 1/5

⇝ CR = -2/25 × 5

⇝ CR = -2/5

Using formula of GP :-

⇝ S_∞ = a /1 - r , -1 < r < 1

⇝ S = 1/5 ÷ ( 1 - (-2/5))

⇝ S = 1/5 ÷ ( 1 +2/5)

⇝ S = 1/5 ÷ 5/7

⇝ S= 1/7