Question

Show that 11cube + 12cube +13 cube + ...+ 20cube is an odd integer divisible by 5 .

Answer 1

Steps :
1) We know that sum of cubes of n natural numbers is given by
${( \frac{n(n + 1)}{2} )}^{2}$

2) We will use this, to get the required expression :
Required No. = Cubes till 20 numbers - Cubes till 10 numbers

3) To check whether it is odd or even, we will check it's unit digit.
See Pic