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Detailed solution for this.

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Asked by g_archanasharma 16th December 2018, 6:18 PM
Answered by Expert
Answer:
S = 12 + 22x + 32 x2 + 42 x3 +..............             (i)
Multiplying x on both sides,
xS = 12x + 22x2 + 32 x3 + ........                          (ii)
Subtract (ii) from (i)
(1 - x)S = 1 + 3x + 5x2 + 7x3 + ........                  (iii)
x(1 - x)S = x + 3x2 + 5x3 + 7x4 + .........             (iv)
(1 - x)S(1 - x)S = 1 + 2x + 2x2 + 2x3 + .....
(1 - x)2S = 1 + 2x (1 + x + x2 + x3 + .......)
 
Solving it further we get S = (1 + x)/(1 - x)3
Answered by Expert 17th December 2018, 9:59 AM
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