`int nsec^2 n dn`

Let T_r denote the rth term of a G.P. for r=1,2,3, If for some positive integers ma n dn , we have T_m=1//n^2 and T_n=1//m^2 , then find the value of T_(m+n//2.)

Statement1: if n in Na n dn is not a multiple of 3 and (1+x+x^2)^n=sum_(r=0)^(2n)a_r x^r , then the value of sum_(r=0)^n(-1)^r a r^n C_r is zero Statement 2: The coefficient of x^n in the expansion of (1-x^3)^n is zero, if n=3k+1orn=3k+2.

Evaluate: ("lim")_(nvecoo)[1/(n^2)sec^2 1/(n^2)+2//n^2sec^2 4/(n^2)++1/nsec^2 1]

The sum of coefficient in the expansion of (1+a x-2x^2)^n is (a)positive, when a<1a n dn=2k ,k in N (b)negative, when a<1a n dn=2k+1,k in N (c)positive, when a<1a n dn in N (d)zero, when a=1

If tantheta=sqrt(n), where n in N ,geq2,t h e nsec2theta is always a rational number (b) an irrational number a positive integer (d) a negative integer

int_n^(n+1)f(x) dx=n^2+n then int_(-1)^1 f(x) dx =

Suppose for every integer n, .int_(n)^(n+1) f(x)dx = n^(2) . The value of int_(-2)^(4) f(x)dx is :

(lim)_(n to oo)n/(2^n)int_0^2x^n dx equals___

lim_(n to oo) n/(2^n)int_0^2x^n \ dx equals

Let n in N such that n gt 1 . Statement-1: int_(oo)^(0) (1)/(1+x^(n))dx=int_(0)^(1) (1)/((1-x^(n))^(1//n))dx Statement-2: int_a^b f(x)dx=int_(a)^(b) f(a+b-x)dx