The largest real value of `x` such that `sum_(k=0)^4((3^(4-k))/((4-k)!))((x^k)/(k !))=(32)/3` is.

Find the value of lim_(n rarr oo)sum_(k=1)^(n)(k^(2)+k-1)/((k+1)!) .

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

The value of sum_(k=0)^(7)[(((7),(k)))/(((14),(k)))sum_(r=k)^(14)((r ),(k))((14),(r ))] , where ((n),(r )) denotes "^(n)C_(r ) is

Prove that sum_(k=0)^(n) (-1)^(k).""^(3n)C_(k) = (-1)^(n). ""^(3n-1)C_(n)

Find the value of k, such that fog=gof f(x)=2x-k, g(x)=4x+5

The value of sum_(k=1)^(13) (1)/(sin((pi)/(4) + ((k-1)pi)/(6)) sin ((pi)/(4)+ (kpi)/(6))) is equal to

Value of sum_(k=1)^oosum_(r=0)^k1/(3^k)(^k C_r) is 2/3 b. 4/3 c. 2 d. 1

Prove that: sum_(k=1)^(100)sin(k x)cos(101-k)x=50"sin"(101 x)

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....