Question

Prove that 2k/(k+1) +2/(k+1)(k+2)=2(k+1)/k+2​

Answer 1

Answer:

TO PROVE :–

$\frac{2k}{k + 1 } + \frac{2}{(k + 1)(k + 2)} = \frac{2(k + 1)}{k + 2}$

L.H.S. :–

$= \frac{2k}{k + 1} + \frac{2}{(k + 1)(k + 2)} \\ \\ = \frac{2}{k + 1} (k + \frac{1}{k + 2} ) \\ \\ = \frac{2}{k + 1} ( \frac{ {k}^{2} + 2k + 1}{k + 2} ) \\ \\ = \frac{2}{k + 1} ( \frac{ {(k + 1)}^{2} }{k + 2} ) \\ \\ = \frac{2(k + 1)}{k + 2}$

= R.H.S.

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