Coefficient of x100 in 1-1-x-1-x2-1-x3-1-xn is 201 C101-n-100 then n-A- none of theseB- 100C- 200D- 101

The correct option is C 200 Coefficient of x^100 = ^100C_100 + ^101C_100 +…+^ nC_100 =^ n+1C_101 =^ 201C_101⇒ n = 200 ...

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Binomial Theorem for Any Index

Coefficient o...

Question

Coefficient of $x^{100} i n 1 + (1 + x) + (1 + x)^{2} + (1 + x)^{3} \dots (1 + x)^{n}$ is $^{201} C_{101}, (n > 100)$ then n =

100

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200

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101

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none of these

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Similar questions

If |x| < 1 then the coefficient of $x^{n}$ in the expansion

of $(1 + x + x^{2} + . . . . . . .)^{2}$ will be

x^{100}

1 + (1 + x) {(1 + x)}^{2} + . . . . . + {(1 + x)}^{n} (i f n \geq 100)

C_{101}^{201}

\lim_{x \to 1} \frac{x + x^{2} + x^{3} + . . . + x^{n} - n}{x - 1} = 5050

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

| x | < 1

x^{n}

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

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