11.c) Prove that: C0+3C1+5C2+...+(2n+1)Cn=(n+1)2ⁿ If (1+x)ⁿ=C0+C1x+C2x²+...+Cnxⁿ. Binomial Theorem !

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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
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.
C0 + C1 x/2 + C2 x²/3 + C3 x³/4 +....+ Cn xⁿ+¹/n+1 = (1+x)ⁿ+¹ – 1 / (n+1)x; using integration @EAG C0 + C1 x/2 + C2 x²/3 + C3 x³/4 +....+ Cn xⁿ+¹/n+1 = (1+x)ⁿ+¹ – 1 / (n+1)x; using integration @EAG
Binomial Theorem Shortcut formulae | Binomial Theorem Class 11 | Arvind Kalia #shorts Binomial Theorem Shortcut formulae | Binomial Theorem Class 11 | Arvind Kalia #shorts
Prove that :`C_(0)-3C_(1)+5C_(2)- .(-1)^n(2n+1)C_(n)=0` Prove that :`C_(0)-3C_(1)+5C_(2)- .(-1)^n(2n+1)C_(n)=0`
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!
BINOMIAL THEOREM #math BINOMIAL THEOREM #math
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)