`a_n=int_0^(pi/2)(1-sint)^nsin2t dt` ten `lim_(n->oo) Sigma_(n=1)^n a_n/n` is equal to

Let a_(n)=int_(0)^(pi//2)(1-sint )^(n) sin 2t, then lim_(n to oo)sum_(n=1)^(n)(a_(n))/(n) is equal to

Let a_(n)=int_(0)^(pi//2)(1-sint )^(n) sin 2t, then lim_(n to oo)sum_(n=1)^(n)(a_(n))/(n) is equal to

lim_(n->oo) nsin(1/n)

Let: a_n=int_0^(pi/2)(1-sint)^nsin2tdt Then find the value of lim_(n->oo)na_n

Let: a_n=int_0^(pi/2)(1-sint)^nsin2tdt Then find the value of lim_(n->oo)na_n

Let: a_n=int_0^(pi/2)(1-sint)^nsin2tdt Then find the value of lim_(n->oo)na_n

a_ (n) = int_ (0) ^ ((pi) / (2)) (1-sin t) ^ (n) sin2tdt ten lim_ (n rarr oo) sum_ (n = 1) ^ (n) (a_ ( n)) / (n) is equal to

If I_n = int_0^(pi//4) tan^n x dx , then lim_(n to oo) n [I_n + I_(n -2)] equals :

If I_n=int_0^(pi/2) (sin(2n-1)x)/sinx)dx , and a_n=int_0^(pi/2) ((sinntheta)/sintheta)^2 d theta , then a_(n+1)-a_n= (A) I_n (B) 2I_n (C) I_(n+1) (D) 0

If S_n=sum_(k=1)^n a_k and lim_(n->oo)a_n=a , then lim_(n->oo)(S_(n+1)-S_n)/sqrt(sum_(k=1)^n k) is equal to