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C 0 +C 1 x +C 2 x 2 + ----------------+C n x n then prove that C 1 2 +2C 2 2 +3C 3 2 + -------------+nC n 2 = (2n-1)/[(n-1)!] 2

C0 +C1x +C2x2 + ----------------+Cnxn  then prove that C12 +2C22 +3C32 + -------------+nCn2 = (2n-1)/[(n-1)!]2

Grade:11

1 Answers

moumi roy
91 Points
7 years ago
(1+x)^{n}=C_{0}+C_{1}x...C_{1}x^{n}\Rightarrow differentiating w.r.t x\Rightarrow n(1+x)^{n-1}=c_{1}+2c_{2}x+....nc_{n}x^{n-1}\Rightarrow multiplying with (1+x)^{n} \Rightarrow (1+x)^{2n-1}n=(c_{1}+2c_{2}x+....nc_{n}x^{n-1})(C_{0}+C_{1}x...C_{1}x^{n} )\Rightarrow coiff of \mathbf{x^{n-1}} in\mathbf{n (1+x)^{2n-1}}\Rightarrow n*_{n-1}^{2n-1}\textrm{C}
HERE C0=CN &C1=CN-1 FORM IS USED CALCULTING WILL FETCH U THE RESULT.THINK THIS THE ANSWER ONLY.NOT ACCEPTINF LESS THAN 100

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