Prove that `(C_0+C_1)(C_1+C_2)(C_2+C_3)(C_(n-1)+C_n)=(n+1)^n/(n!).c_0.C_1.C_2...........C_n`.

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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 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)!)
Prove that : C_0 - C_1/2 + C_2/3- …… + 〖(-1)〗^n C_n/(n+1) = 1/(n+1) Prove that : C_0 - C_1/2 + C_2/3- …… + 〖(-1)〗^n C_n/(n+1) = 1/(n+1)
Prove that : C_1/C_0 + 〖2C〗_2/C_1 + 〖3C〗_3/C_2 +……+ 〖nC〗_n/C_(n-1) = (n(n+1))/2 Prove that : C_1/C_0 + 〖2C〗_2/C_1 + 〖3C〗_3/C_2 +……+ 〖nC〗_n/C_(n-1) = (n(n+1))/2
Prove that : √(C_1 ) + √(C_2 ) + √(C_3 ) + …… + √(C_n ) ≤ 2^(n-1) + (n-1)/2 Prove that : √(C_1 ) + √(C_2 ) + √(C_3 ) + …… + √(C_n ) ≤ 2^(n-1) + (n-1)/2
`C_0/(1.2)+C_1/(2.3)+C_2/(3.4)+........C_n/((n+1)(n+ 2))=` `C_0/(1.2)+C_1/(2.3)+C_2/(3.4)+........C_n/((n+1)(n+ 2))=`
If C_0, C_1, C_2,………C_n are binomial coefficients int eh expansion of (1+x)^n then and n is even... If C_0, C_1, C_2,………C_n are binomial coefficients int eh expansion of (1+x)^n then and n is even...