sum_(k=1)^(2n+1)(-1)^(k-1)*k^(2)=

If for n in N ,sum_(k=0)^(2n)(-1)^k(^(2n)C_k)^2=A , then find the value of sum_(k=0)^(2n)(-1)^k(k-2n)(^(2n)C_k)^2dot

If for n in N ,sum_(k=0)^(2n)(-1)^k(^(2n)C_k)^2=A , then find the value of sum_(k=0)^(2n)(-1)^k(k-2n)(^(2n)C_k)^2dot

Let S_(n)=sum_(k=1)^(4n)(-1)^((k(k+1))/(2))*k^(2) , then S_(n) can take value

Let S_(n)=sum_(k=1)^(4n)(-1)^((k(k+1))/(2))*k^(2) , then S_(n) can take value

Let S_(n)=sum_(k=1)^(4n)(-1)^((k(k+1))/2)k^(2) . Then S_(n) can take values

Evaluate the sum , sum_(k=1)^(n)(1)/(k(k+1)(k+2)……..(k+r)) .

Let X_(k) be real number such that X_(k)gtk^(4)+k^(2)+1 for 1 le k le 2018 . Denot N =sum_(k=1)^(2018)k . Consider the following inequalities: I. (sum_(k=1)^(2018)kx_(k))^(2)leN(sum_(k=1)^(2018)kx_(k)^(2)) " " II. (sum_(k=1)^(2018)kx_(k))^(2)leN(sum_(k=1)^(2018)k^(2)x_(k)^(2))

Let U_(n)=sum_(k=1)^(n)(n)/(n^(2)+k^(2)),S_(n)=sum_(k=0)^(n-1)(n)/(n^(2)+k^(2)) then