Harmonic Progression

Given that the fourth term of a harmonic progression is 1/12 and its ninth term is 1/27, find the tw...

If a, b, c are in HP, then b equals

The general term of a series is given by T_k = k(k+2); evaluate the sum of the first n terms of this...

Determine the exact value of the convergent infinite sum whose kth term is k/2^k, taken over all pos...

Assertion: the series with terms 1/n diverges; Reason: every series whose terms tend to zero must co...

The sum of the first n terms of a certain sequence equals S_n = 3n^2 + 5n for every positive integer...

If the numbers a, b, c are simultaneously in arithmetic progression and in geometric progression wit...

If positive numbers x, y, z are in geometric progression, then the logarithms log x, log y, log z to...

Determine the sum to \infty of the arithmetico-geometric series 1 + 2x + 3x^2 + 4x^3 + ... when the...

A worker is paid 200 rupees in the first month and receives an increment of 25 rupees each subsequen...

Consider the infinite geometric series 9 - 6 + 4 - 8/3 + ... that converges; what is its exact sum t...

Three numbers are in geometric progression, their product equals 216, and the sum of the outer two n...