`sum_(k=1)^19((-2)^k)/(k !(19-k)!)=(-lambda)/(19 !)`

Evaluate : sum_(k=1)^n (2^k+3^(k-1))

Evaluate : sum_(k=1)^n (2^k+3^(k-1))

If lim_(n to oo) sum_(k=2)^(n)cos^(-1)((1+sqrt((k-1)(k+2)(k+1)k))/(k(k+1)))=(120pi)/(lambda) , find the value of lambda .

If lim_(n to oo) sum_(k=2)^(n)cos^(-1)((1+sqrt((k-1)(k+2)(k+1)k))/(k(k+1)))=(120pi)/(lambda) , find the value of lambda .

If lim_(n to oo) sum_(k=2)^(n)cos^(-1)((1+sqrt((k-1)(k+2)(k+1)k))/(k(k+1)))=(120pi)/(lambda) , find the value of lambda .

sum_(k=1)^(20)k[(1)/(k)+(1)/(k+1)+(1)/(k+2)+......+(1)/(20)]

sum_ (k = 1) ^ (n) (2 ^ (k) + 3 ^ (k-1))

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

Find sum_(k=1)^ntan^(- 1)(2k)/(2+k^2+k^4)

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))