The sum ∑ n = 1 21 3 4 n - 1 4 n + 3 is equal to

∑ n = 1 21 3 4 n - 1 4 n + 3 = 3 4 ∑ n = 1 21 1 4 n - 1 - 1 4 n + 3 = 3 4 1 3 - 1 7 + 1 7 - 1 11 + … . + 1 83 - 1 87 = 3 4 1 3 - 1 87 = 3 4 84 261 = 7 29

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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesSpecial sequences/seriesEasy2 minPYQ_2022

MathematicsEasystatement

The sum $\sum_{n = 1}^{21} \frac{3}{(4 n - 1) (4 n + 3)}$ is equal to

Options:

Answer:

Solution:

$\sum_{n = 1}^{21} \frac{3}{(4 n - 1) (4 n + 3)} = \frac{3}{4} \sum_{n = 1}^{21} (\frac{1}{4 n - 1} - \frac{1}{4 n + 3})$
$= \frac{3}{4} [(\frac{1}{3} - \frac{1}{7}) + (\frac{1}{7} - \frac{1}{11}) + \dots . + (\frac{1}{83} - \frac{1}{87})]$
$= \frac{3}{4} [\frac{1}{3} - \frac{1}{87}] = \frac{3}{4} \frac{84}{261} = \frac{7}{29}$

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:Special sequences/series

⏱ 2mℹ️ Source: PYQ_2022

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