The sum of infinite terms of the progression $1 + 3 x + 5 x^{2} + 7 x^{3} + . . . . . . . (| x | < 1)$ ?

\frac{1 + x}{1 - x}

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(\frac{1 + x}{1 - x})

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\frac{1 + x}{(1 - x)^{2}}

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Solution

The correct option is C $\frac{1 + x}{(1 - x)^{2}}$
Sn = 1 + 3x + 5x² + 7x³ +

xSn = x + 3x² + 5x³ +

Sn(1-x) = 1 + 2x + 2x² + 2x³

Sn(1-x) = 1 + 2x(1 + x + x² + x² +

Sn(1-x) = 1 + 2x(1/(1-x))

Sn(1-x) = (1+x)/(1-x)

Sn = (1+x)/(1-x)²

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Similar questions

1 + 3 x + 5 x^{2} + 7 x^{3} + \dots \dots + \infty (H f | x | < 1)

i n f i n i t e

1 + 3 x + 5 x^{2} + 7 x^{3} + . . . ., | x | < 1

1 - 3 x + 5 x^{2} - 7 x^{3} + \dots \infty

| x | < 1

1 + 3 x + 5 x^{2} + 7 x^{3} + 9 x^{4} + . . . . .

(x < 1)

1 - 3 x + 5 x^{2} - 7 x^{3} + \dots \infty

| x | < 1

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