Question

Find tha value of:

$\frac{160}{2 \times 7} + \frac{160}{7 \times 12} + \frac{160}{12 \times 17} + \frac{160}{17 \times 22} + \frac{160}{22 \times 27} + \frac{160}{27 \times 32}$
Answer it with steps.

Answer 1

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Answer 2

$Given : \frac{160}{2 * 7} + \frac{160}{7 * 12} + \frac{160}{12 * 17} + \frac{160}{17 * 22} + \frac{160}{22 * 27} + \frac{160}{27 * 32}$

$= \ \textgreater \ \frac{160}{14}(1 + \frac{1}{6}) + \frac{160}{34} ( \frac{1}{6} + \frac{1}{11}) + \frac{160}{54}( \frac{1}{11} + \frac{1}{16})$

$= \ \textgreater \ \frac{40}{3} + \frac{40}{33} + \frac{5}{11}$

LCM = 33

$= \ \textgreater \ \frac{40 * 11 + 40 + 3 * 5}{33}$

$= \ \textgreater \ \frac{440 + 40 + 15}{33}$

$= \ \textgreater \ \frac{495}{33}$

$= \ \textgreater \ 15$


Therefore the final answer is 15.

Hope this helps!