If (1 + x) (1 + x + x^2) (1 + x + x^2 + x^3) ...... (1 + x + x^2 + x^3 + ...... + x^n) equiv a

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7.Binomial Theorem

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If $(1 + x) (1 + x + x^2) (1 + x + x^2 + x^3) ...... (1 + x + x^2 + x^3 + ...... + x^n)$

$\equiv a_0 + a_1x + a_2x^2 + a_3x^3 + ...... + a_mx^m$ then $\sum\limits_{r\, = \,0}^m {\,\,{a_r}}$ has the value equal to

A

$n!$

B

$(n + 1) !$

C

$(n - 1)!$

D

none

Solution

For the sum of the coefficients, we substitute $x =1 .$

Then we get

$2 \times 3 \times 4 \ldots \times n \times(n+1)$

$=(n+1) !$

Hence $k=1$

Standard 11

Mathematics

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