If `underset(k=0)overset(n)(sum)(k^(2)+k+1)k! =(2007).2007!`, then value of n is

If sum_(k=0)^(n)(k^(2)+k+1)(k!)=(2018)(2018!) then the value of n is equal to

If S_(n)=underset(k=1)overset(4n)sum(-1)^((k(k+1))/(2)).k^(2) then the possible values of s_(n) are-

Evaluate underset(K=1)overset11sum(2+3^K)

If underset(k = 1)overset(n)sumtan^(-1)((1)/(k^(2)+k+1))= tan^(-1)(theta) , " then " theta =

Let S_n=underset(k=1)overset(4n)Sigma (-1)^((k(k+1))/2)k^2 .Then S_n can take value (s)

Let S_n=underset(k=1)overset(4n)Sigma (-1)^((k(k+1))/2)k^2 .Then S_n can take value (s)

Let S_(k)=underset(ntooo)limunderset(i=0)overset(n)sum(1)/((k+1)^(i))." Then "underset(k=1)overset(n)sumkS_(k) equals

Prove that underset(r=1)overset(k)sum(-3)^(r-1) .^(3n)C_(2r-1) = 0 , where k = (3n)/2 and n is an even integer.