`n^n((n+1)/2)^(2n)l s(n in N)`

If S_(n)=1 + (1)/(2) + (1)/(2) + …..+ (1)/(2^(n-1)), (n in N) then …….

The range of f(x)=[1+sinx]+[2+s in2/x]+[3+s in x/3]++[n+s in x/n]AAx in [0,pi] , where [.] denotes the greatest integer function, is, {(n+n-2^2)/2,(n(n+1))/2} {(n(n+1))/2} {(n^2+n-2^)/2,(n(n+1))/2(n^2+n+2)/2} [(n(n+1))/2,(n^2+n+2)/2]

If 1+ 5+ 12+ 22 + 35+ ….. + to n terms = ( n^(2) (n+1) )/(2) then n^( th) term of L.H.S is

1+n. (2n)/(1+n)+(n(n+1))/(1.2) ((2n)/(1+n))^2+…..

1+n. (2n)/(1+n)+(n(n+1))/(1.2) ((2n)/(1+n))^2+…..

The sum S_(n) where T_(n) = (-1)^(n) (n^(2) + n +1)/( n!) is

The sum S_(n) where T_(n) = (-1)^(n) (n^(2) + n +1)/( n!) is

If l_(n)=intcos^(n)xdx, prove that l_(n)=(1)/(n)(cos^(n-1)xsinx)+((n-1)/(n))l_(n-2) .

If L=lim_(n rarr oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+(n)/(n^(2)+3^(2))+....+(1)/(5n)) then the value of tan L=