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

sum_(r=0)^(n)(-1)^(r)*^(n)C_(r)(1+r log_(e)10)/((1+log_(e)10^(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)*^(n)C_(r)(1+r ln10)/((1+ln10^(n))^(r))

Let for n in N, f(n)=sum_(r=0)^(n)(-1)^(r)(C_(r)2^(r+1))/((r+1)(r+2))

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)}