Jee Main
Sequences And Series
JEE Main 2023 (Online) 24th January Morning Shift
INTEGER+4 / -12023
The 4\(^\mathrm{th}\) term of GP is 500 and its common ratio is \(\frac{1}{m},m\in\mathbb{N}\). Let \(\mathrm{S_n}\) denote the sum of the first n terms of this GP. If \(\mathrm{S_6 > S_5 + 1}\) and \(\mathrm{S_7 < S_6 + \frac{1}{2}}\), then the number of possible values of m is ___________