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)` ...

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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)( 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 + 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)
Prove that : C_0+2C_1+3C_2+………..+(n+1) C_n= (n+2)2^(n-1) Prove that : C_0+2C_1+3C_2+………..+(n+1) C_n= (n+2)2^(n-1)
Prove that : C_0 C_1+C_1 C_2+C_2 C_3+……..+C_(n-1) C_n= (2n)!/((n+1)!(n-1)!) Prove that : C_0 C_1+C_1 C_2+C_2 C_3+……..+C_(n-1) C_n= (2n)!/((n+1)!(n-1)!)
if (1+x)^n = C0+C1x+C2x^2+..... +Cnx^n , then prove that C1-2C2+3C3..... +(-1)^(n-1)nCn = 0. if (1+x)^n = C0+C1x+C2x^2+..... +Cnx^n , then prove that C1-2C2+3C3..... +(-1)^(n-1)nCn = 0.
NEB Grade 12 Binomial theorem - C_1+2C_2+3C_3+..........+nCn = n2^(n-1) NEB Grade 12 Binomial theorem - C_1+2C_2+3C_3+..........+nCn = n2^(n-1)
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