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

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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
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one year 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
```
one year ago
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