Let `S n=sum_(k=0)^n1/(sqrt(k+1)+sqrt(k))` What is the value of `sum_(n=1)^99 1/(s_n+s_(n-1))?`

Let S _(n ) = sum _( k =0) ^(n) (1)/( sqrt ( k +1) + sqrt k) What is the value of sum _( n =1) ^( 99) (1)/( S _(n ) + S _( n -1)) ?=

Find the value of sum_(i=1)^n sum_(i=1)^n sum_(k=1)^n k

If n in N, sum_(k=1)^(n)cos^(-1)(x_(k))=npi then the value of sum_(k=1)^(n)sin^(-1)(x_(k))=

If sum_(k=1)^(n)k=45, find the value of sum_(k=1)^(n)k^(3).

If sum_(k=1)^(n)k=210, find the value of sum_(k=1)^(n)k^(2).

If n in N, sum_(k=1)^(n)sin^(-1(x_(k))=(npi)/2 then the value of sum_(k=1)^(n)x_(k)=

Let a_(n)=sum_(k=1)^(n)(1)/(k(n+1-k)), then for n>=2

Let f(n)=sum_(k=-n)^(n)(cot^(-1)((1)/(k))-tan^(-1)(k)) such that sum_(n=2)^(10)(f(n)+f(n-1))=a pi then find the value of (a+1) .