Solveeit Logo
Login

Question

Question: The sum to infinity of series : 1+ \(\frac { 4 } { 5 }\)+ \(\frac { 7 } { 5 ^ { 2 } }\)+ \(\frac { 1...

The sum to infinity of series : 1+ 45\frac { 4 } { 5 }+ 752\frac { 7 } { 5 ^ { 2 } }+ 1053\frac { 10 } { 5 ^ { 3 } }…

A

16/35

B

11/8

C

35/16

D

None

Answer

35/16

Explanation

Solution

Here AP : a = 1 : d = 3 & GP : x = 1 ; r = 1/5

Now S = + = 11−1/5\frac { 1 } { 1 - 1 / 5 } + 3/5(1−1/5)2\frac { 3 / 5 } { ( 1 - 1 / 5 ) ^ { 2 } }

= 54+1516\frac { 5 } { 4 } + \frac { 15 } { 16 }= 3516\frac { 35 } { 16 }