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Let Un=n!/(n+2)! , If Sn=summation n=1 to n Un then Lim n-->infinity Sn equals

Let Un=n!/(n+2)! , If Sn=summation n=1 to n Un then Lim n-->infinity Sn equals

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Grade:11

2 Answers

Nived
14 Points
2 years ago
Un=1/(n+1)(n+2)=(n+2)–(n+2)/(n+1)(n+2)
=1/(n+1)–1/(n+2)
Sn =1/2–1/3+1/3–1/4.....+1/(n+1)–1/(n+2)
=1/2–1/(n+2)
Lim Sn = 1/2–lim 1/(n+2)
=1/2–0=1/2
Vikas TU
14149 Points
2 years ago
Dear student 
We can say that , Un = n!/(n+2)!
So, by expanding this Un we get 
Un = n!/(n+1)(n+2)n!
Cancel the n! ,term on both nimerator and denominator. 
 
Un=1/(n+1)(n+2)=(n+2)–(n+2)/(n+1)(n+2)
=1/(n+1)–1/(n+2)
Sn =1/2–1/3+1/3–1/4.....+1/(n+1)–1/(n+2)
=1/2–1/(n+2)
Lim Sn = 1/2–lim 1/(n+2)
=1/2–0=1/2

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