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$$\lim_{n\to\infty}\frac{1}{n+2}-\frac{1}{2(n+1)}$$

Having difficulty with the limit. Would this be solveable, by writing all terms individually, cancelling out; then attempting to find a convinient form?

I am particularly interested in whether this converges...

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    Are you familiar with the algebra of limits?2012-09-06
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    i am aware of basic series, geometric and the like only. also i have some understanding that the harmonic series diverges, and that possibly the difference may be convergent.2012-09-06
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    It's very easy to show $0\le \frac{1}{n+2}-\frac{0.5}{n+1} \le \frac{1}{n+2}$ for all $n\ge 0$, and since the right-hand side of this squeeze goes toward $0$...2012-09-06
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    ah thankyou. somehow i was reading the lim as if it were sigma the sum! (facepalm) much easier as a limmit. thanks2012-09-06
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    http://sun.iwu.edu/~lstout/limitTheorems/node3.html Read Theorem 3.1 (but don't read the proof... it's probably too advanced for you.) The "a" they use means a real number, but it can also be +infinity or -infinity, as in your example.2012-09-06

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