Question

Find sum to infinity of the series
1/8 - 1/9 +1/16 + 1/27 + 1/32 - 1/81 + .....................

Answer 1

Given :   1/8 - 1/9 +1/16  - 1/27 + 1/32 - 1/81 +  ....................

To Find  : sum to infinity of the series

Solution:

1/8 - 1/9 +1/16  - 1/27 + 1/32 - 1/81 +  ....................

= ( 1/8 + 1/16 + 1/32+ ..........................) - (1/9  + 1/27 + 1/81 +.....................)

Sum of infinity series = a/(1 - r)

a = 1/8  r = 1/2

a = 1/9  r = 1/3

= ( 1/8) /(1 - 1/2)  -  (1/9)/(1 - 1/3)

= 1/4  - 1/6

= 1/12

1/8 - 1/9 +1/16  - 1/27 + 1/32 - 1/81 +  .................... = 1/12

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