True / False For every intger `n >1` , the inequality `(n !)^(1//n)<(n+1)/2` holds

The number of positive integers satisfying the inequality C(n+1,n-2)-C(n+1,n-1)<=100 is

The number of positive integers satisfying the inequality C(n+1,n-2) - C(n+1,n-1)<=100 is

|n-1|lt4 How many integer n satisfy the inequality above?

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

Prove by induction the inequality (1+x)^ngeq 1+n x whenever x is positive and n is a positive integer.

By the principle of mathematical induction prove that for every n in N, the following statements are true: 1 +5 +9 + ....+ (4n - 3) = 2n^2 - n

Statement-1: For every natural number n ge 2, (1)/(sqrt1)+(1)/(sqrt2)+…..(1)/(sqrtn) gt sqrtn Statement-2: For every natural number n ge 2, sqrt(n(n+1) lt n+1

Statement-1: For every natural number nge2 , (1)/(sqrt(1))+(1)/(sqrt(2))+(1)/(sqrt(3))+...+(1)/(sqrt(n))gtsqrt(n) Statement-2: For every natural number nge2, sqrt(n(n+1))ltn+1

The fraction exceeding its own n^(t h) power n in N) by the maximum possible value is (1/n)^(1/(n-1)) (b) (1/n)^(n-1) (1/n)^n (d) (1/n+1)^(1/(n-1))

Assertion: If n is an even positive integer n then sum_(r=0)^n ("^nC_r)/(r+1) = (2^(n+1)-1)/(n+1) , Reason : sum_(r=0)^n ("^nC_r)/(r+1) x^r = ((1+x)^(n+1)-1)/(n+1) (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.