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The sum $S$ = $\frac{1}{9!} + \frac{1}{3! 7!} + \frac{1}{5! 5!} + \frac{1}{7! 3!} + \frac{1}{9!}$ equals

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2910!

2108!

2119!

2107!

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Correct option is A

We can write S as followsS=110! 10C1+10C3+10C5+10C7+10C9=110!29

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The sum S = 19!+13!7!+15!5!+17!3!+19! equals

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The sum $S$ = $\frac{1}{9!} + \frac{1}{3! 7!} + \frac{1}{5! 5!} + \frac{1}{7! 3!} + \frac{1}{9!}$ equals