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Grade 11Differential Calculus

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

Question image for Let Un=n!/(n+2)! , If Sn=summation n=1 to n Un the
Profile image of Ajudiya Janvi
8 Years agoGrade 11
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2 Answers

Profile image of Nived
6 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
Profile image of Vikas TU
6 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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