Question

1/7! + 1/8! = N/9! what is the value of N​

Answer 1

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Answer 2

$Given \: \frac{1}{7!} + \frac{1}{8!} = \frac{N}{9!}$

$\implies \frac{1}{7!} + \frac{1}{8\times 7!} = \frac{N}{9\times 8 \times 7!}$

/* Multiplying both sides by 7! , we get */

$\implies \frac{7!}{7!} + \frac{7!}{8\times 7!} = \frac{7! \times N}{9\times 8 \times 7!}$

$\implies 1 + \frac{1}{8} = \frac{N}{9\times 8 }$

$\implies \frac{8+1}{8} = \frac{N}{72 }$

$\implies \frac{9}{8} = \frac{N}{72 }$

$\implies \frac{9 \times 72}{8} = N$

$\implies 9 \times 9 = N$

$\implies N = 81$

Therefore.,

$\red{ Value \:of \:N} \green {= 81}$

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