JEE MainMathematicsModerateBinomial Theorem

The sum of the
series $\ ^{20}C_{0} - \ ^{20}C_{1} + \ ^{20}C_{2} - \ ^{20}C_{3} + \ldots + \ ^{20}C_{10}\ is\$

Show answer and solution

(1 + x)^{20} = \ ^{20}C_{0} + \ ^{20}C_{1}x + \ ^{20}C_{2}x^{2} +

.....

\ ^{20}C_{20}x^{20}

is
Put x = - 1

\Rightarrow 0 = \ ^{20}C_{0} - \ ^{20}C_{1} + \ ^{20}C_{2}

.........

- \ ^{20}C_{9} + \ ^{20}C_{10} - \ ^{20}C_{11} +

.....

+ \ ^{20}C_{20}

\Rightarrow 0 = 2\left( \ ^{20}C_{0} - \ ^{20}C_{1} +_{.}\ldots\ldots.. - \ ^{20}C_{9} + \ ^{20}C_{10} \right) - \ ^{20}C_{10}

Source: Grass-G / M-08 Mathematics Paper 23 October.docx

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