[JEE Advanced 1983] if 1 x n c 0 c 1x c nx n show that the
If $(1+x)^n=C_0+C_1x+\cdots+C_nx^n$, show that the sum of the products of the $C_i$ taken two at a time is $2^{2n-1}-\dfrac{(2n)!}{2(n!)^2}$.
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VAVidaara Admin
✓ Vidaara Team
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· 2d ago
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Answer: Proved.
$\sum_{i<j}C_iC_j=\frac{(\sum C_i)^2-\sum C_i^2}2=\frac{(2^n)^2-\binom{2n}n}2=2^{2n-1}-\frac{(2n)!}{2(n!)^2}$.
JEE Advanced 1983 · Binomial Theorem — verified solution by the Vidaara Team.
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