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Sequences and Series question

2023 · 24 Jan · Shift 1 · Q39

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JEE Main
Mathematics
Sequences and Series
2023 · 24 Jan · Shift 1 · Q39

Sequences and Series question

2023 · 24 Jan · Shift 1 · Q39

JEE MainMathematicsSequences and SeriesNumerical+4 / −1

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 \gt S_5 + 1}

and

\mathrm{S_7 \lt S_6 + \frac{1}{2}}

, then the number of possible values of m is

\underline{\hspace{2cm}}

Numerical answer

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