Prove thart. 1 9! +1 10! +1 11! =122 11! - Vidyadip

Question

Prove thart. $\frac{1}{9!}+\frac{1}{10!}+\frac{1}{11!}=\frac{122}{11!}$

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Answer

$\text{L.H.S.}= \frac{1}{9!}+\frac{1}{10!}+\frac{1}{11!}$$=\frac{1}{9!}+\frac{1}{10\times9!}+\frac{1}{11\times10\times9!}$
$=\frac{11\times10+11+1}{11\times10\times9!}$
$=\frac{110+11+1}{11!}$
$=\frac{122}{11!}$
$\text{R.H.S.}$
Hence, $\frac{1}{9!}+\frac{1}{10!}+\frac{1}{11!}= \frac{122}{11!}$

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