Lf 1-x1-x-x21 -x-x2-x3-1-x-x2-xn-1-ao-a1x-a2x2-ammxm- then a0-a1-a2-am-

The correct option is B n! We have, (1+x)(1+x+x^2)(1 #10;+x+x^2+x^3)…… . +(1+x+x^2+..x^n 1)=a_o+a_1x+a_2x^2+..a_mx^m Put x=1 both sides w ...

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General Solution of a Differential Equation

lf 1+x1+x+x...

Question

lf $(1 + x) (1 + x + x^{2}) (1 + x + x^{2} + x^{3}) \dots + (1 + x + x^{2} + . . x^{n - 1}) = a_{o} + a_{1} x + a_{2} x^{2} + . . a_{m} m x^{m}$ , then $a_{0} + a_{1} + a_{2} + \dots \dots \dots + a_{m} =$

m!

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n!

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\frac{(m!)^{2}}{m! n!}

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n

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\frac{1}{a_{0}} + \frac{x}{a_{0} a_{1}} + \frac{x^{2}}{a_{0} a_{1} a_{2}} + \dots + \frac{x^{n}}{a_{0} a_{1} a_{2} \dots a_{n}} = \frac{1}{a_{0} -} \frac{a_{0} x}{a_{1} + x -} \frac{a_{1} x}{a_{2} + x -} \dots \frac{a_{n - 1} x}{a_{n} + x}

(1 + x + x^{2}) (1 - \frac{x}{1!} + \frac{x^{2}}{2!} - \frac{x^{3}}{3!} + \dots) = a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3} + a_{4} x^{4} + . . .

{log}_{e} (1 + x + x^{2} + x^{3}) = a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3} + \dots

a_{1}

a_{2}

(1 \times x) (1 + x + x^{2}) (1 + x + x^{2} + x^{3}) . . . . . (1 + x + x^{2} + x^{3} + . . . . . . + x^{n}) \equiv

a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3} + . . . . . . . a_{m} x^{m}

m \sum r = 0 a_{r}

(n + k)!

k

(1 + x) (1 + x + x^{2}) (1 + x + x^{2} + x^{3}) . . . . . . (1 + x + x^{2} + . . . . + x^{30}) = a_{0} + a_{1} x + a_{2} x^{2} + . . . . . . . . + a_{465} x^{465}

a_{0} + a_{2} + a_{4} + . . . . . . . . + a_{464}

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