Let, `C_(k) = ""^(n)C_(k) " for" 0 le kle n and A_(k) = [[C_(k-1)^(2),0],[0,C_(k)^(2)]]` for
`k ge l and `
`A_(1) + A_(2) + A_(3) +...+ A_(n) = [[k_(1),0],[0, k_(2)]]`, then

Let C_k = .^nC_k, for 0 lt= k lt=n and A_k = ((C_(k-1)^2,0), (0,C_k^2)) for k gt= 1 and A_1+A_2+...+A_n = ((k_1,0), (0,k_2)), then

Let a_(k)=.^(n)C_(k) for 0<=k<=n and A_(k)=[[a_(k-1),00,a_(k)]] for 1<=k<=n and B=sum_(k=1)^(n-1)A_(k)*A_(k+1)=[[a,00,b]]

If a_(k)=(1)/(k(k+1)) for k=1,2,3, .. , n, then (sum_(k=1)^(n) a_(k))^(2)=

If a_(k) = (1)/( k(k+1) ) for k= 1,2,3,….n then (sum_(k=1)^(n) a_(k) )=

a_(k)=(1)/(k(k+1)) for k=1,2,3,4,...n then (sum_(k=1)^(n)a_(k))^(2)=

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=

Let a_(1), a_(2), a_(3),...,a_(49) be in AP such that sum_(k=0)^(12) a_(4k +1) = 416 and a_(9) + a_(43) = 66 . If a_(1)^(2) + a_(2)^(2) + ...+ a_(17)^(2) = 140m , then m is equal to