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(C0)^2+ 2 (C1)^2 + 3 (C2)^2 + 4 (C3)^2.....

`(C_0)^2+ 2 (C_1)^2 + 3 (C_2)^2 + 4 (C_3)^2...+(n+1) (c_n)^2`

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C_0 + (C_1)/(2) + (C_2)/(2^2) + (C_3)/(2^3)+…..+(C_n)/(2^n)=

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(1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + … + C_(n) x^(n) , prove that C_(0) - 2C_(1) + 3C_(2) - 4C_(3) + … + (-1)^(n) (n+1) C_(n) = 0

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k. C_0 + k^2 . (C_1)/(2)+k^3. (C_2)/(3)+…..+ k^(n+1). (C_n)/(n+1)=