Find the sum upto n terms of the series 1²+(1²+2²)+(1²+2²+3²)+…….

Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, … is (a) purely real (b) purely imaginary ?

The sum of three numbers in A.P. is 12, and the sum of their cubes is 288. Find the numbers.

Find the sum to n terms of the series:

If S₁,S₂,S₃ are the sums of first n natural numbers, their squares, their cubes respectively. Show that 9S₂²=S₃(1+8S₁)