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[sum(r=0)^(n)(-1)^(r)*^(n)C(r)(1+r*log(e...

[sum_(r=0)^(n)(-1)^(r)*^(n)C_(r)(1+r*log_(e)10)/((1+log_(e)10^(n))^(r))=],[1],[(-1)/(-1)]

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sum_(r=0)^(n)(-1)^(r)*^(n)C_(r)(1+r ln10)/((1+ln10^(n))^(r))

If C_(0),C_(1),C_(2),.........,C_(3) denotes the binomial coeffcients in the expanssion of (1+x)^(a), then sum_(r rarr a)^(a)(-1)^(rn)C_(r).(1+r log_(e)10)/((1+log_(e)10^(x))^(r))=

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

sum_(r= 2)^(43) (1)/(log_(r)n) =

Statement -2: sum_(r=0)^(n) (-1)^( r) (""^(n)C_(r))/(r+1) = (1)/(n+1) Statement-2: sum_(r=0)^(n) (-1)^(r) (""^(n)C_(r))/(r+1) x^(r) = (1)/((n+1)x) { 1 - (1 - x)^(n+1)}

Statement -2: sum_(r=0)^(n) (-1)^( r) (""^(n)C_(r))/(r+1) = (1)/(n+1) Statement-2: sum_(r=0)^(n) (-1)^(r) (""^(n)C_(r))/(r+1) x^(r) = (1)/((n+1)x) { 1 - (1 - x)^(n+1)}

The value of sum_(r=1)^(n)(-1)^(r-1)((r )/(r+1))*^(n)C_(r ) is (a) 1/(n+1) (b) 1/n (c) 1/(n-1) (d) 0

The value of sum_(r=1)^(n)(-1)^(r-1)((r )/(r+1))*^(n)C_(r ) is (a) 1/(n+1) (b) 1/n (c) 1/(n-1) (d) 0