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The sum of the series $S = \frac{1}{19!} + \frac{1}{3! 17!} + \frac{1}{5! 15!} + \dots \dots \dots t o 10$ terms is equal to

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21920!

22020!

21020!

21919!

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detailed solution

Correct option is A

We have,S=119!+13!17!+15!15!+……… to 10 terms S=120!20!1!19!+20!3!17!+20!5!15!+……….t∘10 terms S=120! 20C1+20C3+20C5+………+20C19S=120!220−1=21920!

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The sum of the series S=119!+13!17!+15!15!+………to10 terms is equal to

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The sum of the series $S = \frac{1}{19!} + \frac{1}{3! 17!} + \frac{1}{5! 15!} + \dots \dots \dots t o 10$ terms is equal to