Q.

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

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a

21920!

b

22020!

c

21020!

d

21919!

answer is A.

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Detailed Solution

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