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SSC MTS 2026 PYQ — Question 16

SSC MTS - 5 Feb 2026 - Shift 1 • Quantitative Aptitude • Q16

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115+135+163+⋯+1195=?\frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \dots + \frac{1}{195} = ?

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Correct answer: B

Explanation

115+135+163+⋯+11951n(n+2)=12(1n−1n+2)115=13×5=12(13−15)135=15×7=12(15−17)163=17×9=12(17−19)1195=113×15=12(113−115)=12(13−115)=12×5−115=12×415=215\frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \dots + \frac{1}{195}\\\frac{1}{n(n+2)} = \frac{1}{2} \left( \frac{1}{n} - \frac{1}{n+2} \right)\\\frac{1}{15} = \frac{1}{3 \times 5} = \frac{1}{2} \left( \frac{1}{3} - \frac{1}{5} \right) \\ \frac{1}{35} = \frac{1}{5 \times 7} = \frac{1}{2} \left( \frac{1}{5} - \frac{1}{7} \right) \\ \frac{1}{63} = \frac{1}{7 \times 9} = \frac{1}{2} \left( \frac{1}{7} - \frac{1}{9} \right)\\\frac{1}{195} = \frac{1}{13 \times 15} = \frac{1}{2} \left( \frac{1}{13} - \frac{1}{15} \right)\\= \frac{1}{2} \left( \frac{1}{3} - \frac{1}{15} \right) \\ = \frac{1}{2} \times \frac{5 - 1}{15} \\ = \frac{1}{2} \times \frac{4}{15} \\ = \frac{2}{15}