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If | x | <1, then the co-efficient of x^n in the expansion of

Question

If $∣ x ∣ < 1$ , then the co-efficient of $x^{n}$ in the expansion of $(1 + x + x^{2} + x^{3} + ......)^{2}$ is

n

n - 1

n - 2

n + 1

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Camila Discussed

∣ x ∣ < 1

, then the co-efficient of

x^{n}

in the expansion of

(1 + x + x^{2} + x^{3} + ......)^{2}

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

Let

S = (1 + x + x^{2} + x^{3} + ....)^{2}

1 + x + x^{2} + ...

is in G.P

∴ S_{n} = \frac{1}{1 - x} = (1 - x)^{- 1}

Now,

S = [(1 - x)^{- 1}]^{2}

= (1 - x)^{- 2}

= 1 + 2 x + 3 x^{2} + 4 x^{3} + .... + (n + 1) x^{n} + ...

∴

co-efficient of

x^{n}

n + 1

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Question Text	If $∣ x ∣ < 1$ , then the co-efficient of $x^{n}$ in the expansion of $(1 + x + x^{2} + x^{3} + ......)^{2}$ is
Answer Type	Text solution:1
Upvotes	150