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Find the infinite sum of the series

$1 + \frac{4}{7} + \frac{9}{7^2} + \frac{16}{7^3} + \frac{25}{7^4} + .............\Join$
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let x= 1+4/7+9/72+16/73+25/74..................................@1

now multiply x by 1/7.

x/7= 1/7 + 4/72 + 9/73+16/74..................................@2

subtracting @1 from @2 we get..

6x/7= 1 + 3/7 +5/72 + 7/73 + 9/74............................@3

now multiply @3 by 1/7 we get..

6x/49= 1/7 +3/72 + 5/73 + 7/74 ..............................@4

subtracting @4 from @3 we get,

36x/49= 1+2/7 + 2/72 + 2/73 +2/74...............................infinity

36x/49= 1+ 2/7( 1/(1-1/7))

           = 1+ 1/3 =4/3

x= 4/3 *49/36 = 49/27 answer

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