The GCD of `a^(k),a^(k+1),a^(k+5)` where `k epsilon N`

The L.C.M. of a^(k), a^(k + 3), a^(k + 5) where k in N is …………… .

The value of Sigma_(k=0)^(n)(i^(k)+i^(k+1)) , where i^(2)=-1 , is equal to

If lim_(n rarr oo)(prod_(k-1)^(n)(1+(k)/(n)))^(1/n) has the value of equal to ke^(-1) where k in N, find k

The value of sum_(k=0)^(n)(i^(k)+i^(k+1)) , where i^(2)= -1 , is equal to

" If "Lt_(nrarroo) ((prod_(k=1)^(n)(1+(k)/(n))))^(1/n)" has the value of equal to "ke^(-1)" where "k in N" ,then the value of "K" is "

If A=[{:(3,-4),(1,-1):}] then show that A^(k)=[{:(1+2k,-4k),(k,1-2k):}],k epsilon N

If the lines barr = (2, -3, 7) + k(2, a, 5), k epsilon R and barr = (1, 2, 3) + k(3, -a, a), k epsilon R are perpendicular to each other then a = ......

If lim_(n->oo)(1(2n-1)^(k)+2(2n-2)^(k)+3(2n-3)^(k)+...+n.n^(k))/(n^(k+1))=(2^(k+a)-2)/(k+1)+(1-2^(k+b))/(k+2) where a, b, k in N and k >= 5 then the value of (a+b)/(3) is

If lim_(n->oo)(1(2n-1)^(k)+2(2n-2)^(k)+3(2n-3)^(k)+...+n.n^(k))/(n^(k+1))=(2^(k+a)-2)/(k+1)+(1-2^(k+b))/(k+2) where a, b, k in N and k >= 5 then the value of (a+b)/(3) is

If lim_(n->oo)(1(2n-1)^(k)+2(2n-2)^(k)+3(2n-3)^(k)+...+n.n^(k))/(n^(k+1))=(2^(k+a)-2)/(k+1)+(1-2^(k+b))/(k+2) where a, b, k in N and k >= 5 then the value of (a+b)/(3) is