" 5."tan(x+4x+9x+....+n^(2)x)(n" any positive integer ")

Find the period of tan(x+4x+9x+.......+n^2x) (n any positive integer)

Period of tan(x+4x+9x+....n^(2)x) is

Prove that (""^n C_0)/x-(""^n C_1)/(x+1)+(""^n C_2)/(x+2)-.....+(-1)^n(""^n C_n)/(x+n)=(n !)/(x(x+1) . . . (x-n)), where n is any positive integer and x is not a negative integer.

Prove that (nC_(0))/(x)-(n_(C_(0)))/(x+1)+(^nC_(1))/(x+2)-...+(-1)^(n)(n_(n))/(x+n)=(n!)/(x(x+1)...(x-n)) where n is any positive integer and x is not a negative integer.

In the expansion of (x^(2)+(2)/(x))^(n) for positive integer n has a term independent of x, then n is

If rArr I_(n)=int_(0)^(pi//4) tan ^(n)x dx , then for any positive integer, n, the value of n(I_(n+1)+I_(n-1)) is,

If ((1+i)/(1-i))^x=1 then (A) x=2n+1 , where n is any positive ineger (B) x=4n , where n is any positive integer (C) x=2n where n is any positive integer (D) x=4n+1 where n is any positive integer

Use factor theorem to prove that (x+a) is a factor of (x^(n)+a^(n)) for any odd positive integer n .