Let Un=n!/(n+2)! , If Sn=summation n=1 to n Un then Lim n-->infinity Sn equals
Ajudiya Janvi , 7 Years ago
Grade 11
Differential Calculus> Let Un=n!/(n+2)! , If Sn=summation n=1 to...
2 AnswersNived
Last Activity: 5 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
Last Activity: 5 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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