find the sum of n terms of :- 1/2*5+1/5*8+1/8*11+ - Maths - Sequences and Series

Question

find the sum of n terms of :- 1/2*5+1/5*8+1/8*11+

Sunanta Meitei · Accepted Answer

The given series is $\frac{1}{2 \times 5} + \frac{1}{5 \times 8} + \frac{1}{8 \times 11} + ....$

$H e r e, n^{t h} t e r m (a_{n}) = \frac{1}{(3 n - 1) \times (3 n + 2)} = \frac{1}{3} [\frac{1}{(3 n - 1)} - \frac{1}{(3 n + 2)}] (P a r t i a l F r a c t i o n) . a_{1} = \frac{1}{3} (\frac{1}{2} - \frac{1}{5}), a_{2} = \frac{1}{3} (\frac{1}{5} - \frac{1}{8}), a_{3} = \frac{1}{3} (\frac{1}{8} - \frac{1}{11}), ... B y a d d i n g, w e g e t, S_{n} = a_{1} + a_{2} + a_{3} + ... = \frac{1}{3} [(\frac{1}{2} - \frac{1}{5}) + (\frac{1}{5} - \frac{1}{8}) + ... + (\frac{1}{(3 n - 1)} - \frac{1}{(3 n + 2)})] = \frac{1}{3} (\frac{1}{2} - \frac{1}{(3 n + 2)})$

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