Find the value of `sum_(1le i,)sum_(jle n)(1)`.

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

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

Prove the following sum_(1le i) sum_(lt j le n) (i+j)=(n(n^(2)-1))/(2)

Find the value of sum_(k=1)^(10){sin((2kpi)/(11))-i cos ((2kpi)/(11))}

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

The value of sum_(n= 1)^(13) (i^(n) + i^(n + 1)) , where i=sqrt(-1) is

If (1+x)^(n)=sum_(r=0)^(n)""^(n)C_(r )x^(r ) and if sum_(r=0)^(n) (1)/(""^(n)C_(r ))=lambda , then show that sum_(0 leilen) sum_(0 le j len) ((i)/(""^(n)C_(i)) +(j)/(""^(n)C_(j)))=n(n+1)lambda

If n is a positive integer and C_4 = ""^nC_r then find the value of sum_(x = 1)^n r^2 ((C_r)/(C_(r - 1)) )