If a and b are distinct integers prove that `a-b` is a factor of `a^n-b^n` whenever n is a positive integer.

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

Write the expansion of (a+b)^n , where n is any positive integer.

Prove that the function f(x)=x^n is continuous at x=n, where n is a positive integer.

Prove that 2^n gt n for all positive integtrs n.

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

How many terms are there in the expansion of (1+x)^2n (n is a positive integer)?

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.

if A=[[3, -4],[ 1, (-1)]] , then prove that A^n=[[1+2 n, -4 n ],[n , 1-2n]] where n is any positive integer.

Write the converse of the following statements (iii)If two integers a and b are such that a>b,then a-b is always a positive integer.

Write the converse of the following statements.(iii)If two integers a and b are such that a>b,then a-b is always a positive integer.