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

The inequality n!>2^(n-1) is true

The inequality n ! > 2^(n-1) is true:

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

The number of positive integers satisfying the inequality .^(n+1)C_(n-2) - .^(n + 1)C_(n - 1) le 100 is

Prove that for every positive integer n the following inequality holds true: (1)/(9)+(1)/(25)+…..+(1)/((2n+1)^2)lt(1)/(4) .

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

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