Find the least positive integer n such that `((2i)/(1+i))^(n)` is a positive integer

Which one of the following is true? a) (1+(1)/(n))^(n)ltn^(2),n is a positive integer b) (1+(1)/(n))^(n)lt2,n is a positive integer c) (1+(1)/(n))^(n)ltn^(3),n is a positive integer d) (1+(1)/(n))^(n)ge2,n is a positive integer

For any positive integer n , int (dx)/( x ^(n +1) + x ) is equal to:

If x_(i) = a_(i)b_(i)c_(i)= I = 1,2,3 are three - digit positive integers such that each x_(i) is a multiple of 19, then for some interger n, prove that |(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))| is divisible by 19.

Write the expansion of (a-b)^n, n is a positive integer

Expand (1+ax)^n upto the third term if n is a positive integer

Which among the following is the least number that will divide 7^(2n)-4^(2n) for every positive integer n? [4,7,11,13]

Using mathematical induction prove that d/(d x)(x^n)=n x^(n-1) for all positive integers n .

Write the converse of the following statements. (i) If a number n is even, then n^(2) is even. (ii) If you do all the exercises in the book, you get an A grade in the class. (iii) If two inegers a and b are such that agtb , then a-b is alwàys a positive integer.