Find the sum of : the first n positive integers

Find the sum of the first 40 positive integers divisible by 6.

Find the sum of : the first 1000 positive integers

The number of positive integers with the property that they cann be expressed as the sum of the cubes of 2 positive integers in two different ways is

Find the sum of the first a terms of the series whose nth term is: n(n + 3) .

Find the sum of the first n terms of the series: 3+7+13 +21 +31 +...

Find the sum of the first a terms of the series whose nth term is: 3n^2+5 .

If the arithmetic mean of the product of all pairs of positive integers whose sum is n is A_n then lim_(n->oo) n^2/(A_n) equals to

Evaluate the following integrals: intsin mx cos nx dx where m and n are distinct positive integers.

Statement 1 The difference between the sum of the first 100 even natural numbers and the sum of the first 100 odd natural numbers is 100. Statement 2 The difference between the sum opf the first n even natural numbers and sum of the first n odd natural numbers is n.