Let`S_k=([1,k],[0,1])`,k∈N.Then`(S_2)^n(S_k)^-1` (where n in N) is equal to:`(S_k)^-1` denotes the inverse of matrix `S_k`

The value of sum_(r=1)^(n+1)(sum_(k=1)^n "^k C_(r-1)) ( where r ,k ,n in N) is equal to a. 2^(n+1)-2 b. 2^(n+1)-1 c. 2^(n+1) d. none of these

sum _(k=1)^(n) tan^(-1). 1/(1+k+k^(2)) is equal to

Let K be a positive real number and A=[2k-1 2sqrt(k)2sqrt(k)2sqrt(k)1-2k-2sqrt(k)2k-1]a n dB=[0 2k-1sqrt(k)1-2k0 2-sqrt(k)-2sqrt(k)0] . If det (a d jA)+det(a d jB)=10^6,t h e n[k] is equal to. [Note: a d jM denotes the adjoint of a square matix M and [k] denotes the largest integer less than or equal to K ].

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

Find the area in the 1* quadrant bounded by [x]+[y]=n , where n in N and y=k (where k in n AA k<=n+1 ), where [.] denotes the greatest integer less than or equal to x.

Let f(n)= sum_(k=1)^(n) k^2 ^"(n )C_k)^ 2 then the value of f(5) equals

If k in R_o then det{adj(k I_n)} is equal to (A) K^(n-1) (B) K^((n-1)n) (C) K^n (D) k

For what value(s) of k the matrix [(4,k),(2,1)] has no inverse?

Let S_(k) = (1+2+3+...+k)/(k) . If S_(1)^(2) + s_(2)^(2) +...+S_(10)^(2) = (5)/(12)A , then A is equal to

Let S_(k) , where k = 1,2 ,....,100, denotes the sum of the infinite geometric series whose first term is (k -1)/(k!) and the common ratio is (1)/(k) . Then, the value of (100^(2))/(100!) +sum_(k=2)^(100) | (k^(2) - 3k +1) S_(k)| is....