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Sum the series s = 1 + 2x + 3x^2 + 4x^3 +··· , |x| < 1

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Sum the series s = 1 + 2x + 3x2 + 4x3 +··· , |x| < 1

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Best answer

We know that

y = 1 + x + x2 + x3 + x4 +···= 1/(1 − x)

Differentiating with respect to x,

dy/dx = 1 + 2x + 3x2 + 4x3 +···= 1/(1 − x)2 = S

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