If `(1+x)^n=C_0+C_1x+C_2x^2+...+C_nx^n` then the value of `(C_0)^2+(C_1)^2/2+(C_2)^2/3+...+(C_n...

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If `(1+x)^n=c_0+c_1x+c_2x^2+...+c_nx^n` then the value of `c_0+3c_1+5c_2+....+(2n+1)c_n` is- If `(1+x)^n=c_0+c_1x+c_2x^2+...+c_nx^n` then the value of `c_0+3c_1+5c_2+....+(2n+1)c_n` is-
If `(1+x)^n=c_0+C_1x+C_2x^2++C_n x^n `,using derivative prove that `C_1+2C_2++nC_n=n .2^(n-1)` ... If `(1+x)^n=c_0+C_1x+C_2x^2++C_n x^n `,using derivative prove that `C_1+2C_2++nC_n=n .2^(n-1)` ...
Simplify `C_0^2+C_1^2/2+C_2^2/3+...+C_n^2/(n+1)`. Simplify `C_0^2+C_1^2/2+C_2^2/3+...+C_n^2/(n+1)`.
Prove that : (C_0+C_1)( C_1+C_2)( C_2+C_3)……….( C_(n-1)+C_n) = (C_0.C_1.C_2……C_(n-1) 〖(n+1)〗^n)/n! Prove that : (C_0+C_1)( C_1+C_2)( C_2+C_3)……….( C_(n-1)+C_n) = (C_0.C_1.C_2……C_(n-1) 〖(n+1)〗^n)/n!
Prove that : C_0+3C_1+5C_2+…………..+(2n+1) C_n= (n+1) 2^n Prove that : C_0+3C_1+5C_2+…………..+(2n+1) C_n= (n+1) 2^n
prove that : 〖C_0〗^2 + 〖C_1〗^2 +〖C_2〗^2+………+〖C_n〗^2 = (2n)!/n!n! prove that : 〖C_0〗^2 + 〖C_1〗^2 +〖C_2〗^2+………+〖C_n〗^2 = (2n)!/n!n!
if (1+x)^n = C0+C1x+C2x^2+..... +Cnx^n , then prove that (n+2) 2^(n-1) = C0+2C1+3C2+..... +(n+1)Cn. if (1+x)^n = C0+C1x+C2x^2+..... +Cnx^n , then prove that (n+2) 2^(n-1) = C0+2C1+3C2+..... +(n+1)Cn.
Prove that : C_0 + C_1/2 + C_2/3 + …… + C_n/(n+1) = (2^(n+1)-1)/(n+1) Prove that : C_0 + C_1/2 + C_2/3 + …… + C_n/(n+1) = (2^(n+1)-1)/(n+1)