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C0+C1+C2+C3+...........Cn= ?...

`C_0+C_1+C_2+C_3+...........C_n= ?`

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If (1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n prove that : C_0+ C_1/2 +C_2/3+.........+C_n/(n+1)= (2^(n+1)-1)/(n+1) .

C_1/C_0+2C_2/C_1+3C_3/C_2+............+nC_n/C_(n-1)=(n(n+1))/2

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Prove that (C_0+C_1)(C_1+C_2)(C_2+C_3)(C_3+C_4)...........(C_(n-1)+C_n) = (C_0C_1C_2.....C_(n-1)(n+1)^n)/(n!)

Prove that (C_0+C_1)(C_1+C_2)(C_2+C_3)(C_3+C_4)...........(C_(n-1)+C_n) = (C_0C_1C_2.....C_(n-1)(n+1)^n)/(n!)

Show that C_0 C_1 + C_1 C_2 + C_2 C_3 + .... + C_(n-1) C_n = (2n!)/((n-1)!(n+1!))