The value of left( begin{array}{l}300end{arra | vedclass

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Question

(b) ${(1 - x)^{30}} = {\,^{30}}{C_0}{x^0} - {\,^{30}}{C_1}{x^1} + {\,^{30}}{C_2}{x^2} + ...... + {( - 1)^{30}}{\;^{30}}{C_{30}}{x^{30}}$....$(i)$

Vedclass · Accepted Answer

$^{30}{C_{10}}$

Vedclass · Answer

(b) ${(1 - x)^{30}} = {\,^{30}}{C_0}{x^0} - {\,^{30}}{C_1}{x^1} + {\,^{30}}{C_2}{x^2} + ...... + {( - 1)^{30}}{\;^{30}}{C_{30}}{x^{30}}$....$(i)$

${(x + 1)^{30}} = {\,^{30}}{C_0}{x^{30}} + {\,^{30}}{C_1}{x^{29}} + {\,^{30}}{C_2}{x^{28}}+ ...... + {\,^{30}}{C_{10}}{x^{20}} + .... + {\,^{30}}{C_{30}}{x^0}$....$(ii)$

Multiplying (i) and (ii) and equating the coefficient of $x^{20}$ on both sides, we get required sum 

= coefficient of $x^{20}$ in $(1 -x^2)^{30}={^{30}}{C^{10}}$.

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