Find the value of `sum_(n=8)^100[{(-1)^n*n)/2]` where `[x]` greatest integer function

Find the value of sum_(n=0)^(100)i^(n!), where i=sqrt(-1)

If n in N , the value of int_(0)^(n) [x] dx (where [x] is the greatest integer function) is

For a positive integer n, let I _(n) =int _(-pi)^(pi) ((pi)/(2) -|x|) cos nx dx Find the value of [I _(1) + I _(3) +I_(4)] (where [.] denotes greatest integer function) .

Let the sum sum_(n=1)^(9)1/(n(n+1)(n+2)) written in the rational form be p/q (where p and q are co-prime), then the value of [(q-p)/10] is (where [.] is the greatest integer function)

The value of sum_(n=1)^1000 int_(n-1)^n e^(x-[x])dx , where [x] is the greatest integer function, is (A) (e^1000-1)/1000 (B) (e-1)/1000 (C) (e^1000-1)/(e-1) (D) 1000(e-1)

The value of sum_(n=1)^100 int_(n-1)^n e^(x-[x])dx =

Let x=(5+2sqrt6)^(n),ninN , then find the value of x-x^(2)+x[x] , where [.] denotes greatest integer function.

Evaluate lim_(n rarr oo)[sum_(r=1)^(n)(1)/(2^(r))], where [.] denotes the greatest integer function.

Evaluate int_(0)^(a)[x^(n)]dx, (where,[*] denotes the greatest integer function).

If x=(2+sqrt(3))^(n) ,then the value of x-x^(2)+x[x] where [.] denotes the greatest integer function, is equal to