Let S(n)=sum(k=1)^(4n)(-1)^((k(k+1))/(2)...

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

A

Statement-l is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-l

B

Statement-l is Inie, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1

C

Statement-l is True, Statement-2 is False

D

Statement-! is False, Statement-2 is True

Verified by Experts

The correct Answer is:

C

Similar Questions

Explore conceptually related problems

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

If sum_(r=1)^(n) t_(r ) = sum_(k=1)^(n) sum_(j=1)^(k) sum_(i=1)^(j) 2 , then sum_(r=1)^(n) (1)/( t_(r )) equals :

sum_(i=1)^(n) sum_(j=1)^(i)sum_(k=1)^(j) 1 equals :

lim_(n rarr oo) 1/n^(3) sum_(k=1)^(n) k^(2)x =

Evaluate sum_(k=1)^11(2+3^k)

Let (1+x^(2))^(2)(1+x)^(n) = sum_(k=0)^(n+4) a_(k) x^(k) . If a_(1) , a_(2) , a_(3) are in A.P., then n=

lim_(n rarr oo) sum_(r=1)^(n) 1/n sec^(2) ((rpi)/(4n)) =

If 2^(3)+4^(3)+6^(3)+.. .+(2 n)^(3)=k n^(2)(n+1)^(2) then k=

Evaluate S=sum_(n=0)^n(2^n)/((a^(2^n)+1) (where a>1) .

If z_(k)=cos.(pi)/(2^(k))+isin.(pi)/(2^(k)) , k=1,2............ , then the value of z_(1)z_(2) ...............to oo is