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Deduce that: sum(r=0)^n .^nCr (-1)^n 1/(...

Deduce that: `sum_(r=0)^n .^nC_r (-1)^n 1/((r+1)(r+2)) = 1/(n+2)`

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Deduce that: sum_(r=0)^n .^nC_r (-1)^r 1/((r+1)(r+2)) = 1/(n+2)

If x+y=1, prove that sum_(r=0)^n .^nC_r x^r y^(n-r) = 1 .

If x+y=1, prove that sum_(r=0)^n .^nC_r x^r y^(n-r) = 1 .

Prove that sum_(r = 1)^n r^3 ((n_C_r)/(C_(r - 1)))^2 = (n (n + 1)^2 (n+2))/(12)

If (1+x)^n=sum_(r=0)^n C_rx^r then prove that sum_(r=0)^n (C_r)/((r+1)2^(r+1))=(3^(n+1)-2^(n+1))/((n+1)2^(n+1))

sum_(r=1)^(n) (-1)^(r-1) ""^nC_r(a - r) =

sum_(r=1)^(n) (-1)^(r-1) ""^nC_r(a - r) =

sum_(r=0)^n (-1)^r .^nC_r (1+rln10)/(1+ln10^n)^r

Find the sum sum_(r=1)^n r^n (^nC_r)/(^nC_(r-1)) .

Find the sum sum_(r=1)^n r^n (^nC_r)/(^nC_(r-1)) .