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Determine whether or not each of the following infinite series converges, and evaluate it if it does.

• [math]\sum_{k=1}^\infty \frac1{k(k+1)}[/math].
• [math]\sum_{i=1}^\infty \frac{2i+1}{i^2(i^2+2i+1)}[/math].
• [math]\sum_{k=1}^\infty \ln \left(\frac{k+1}k\right) = \ln \left(\frac21\right) + \ln \left(\frac32\right) + \ln \left(\frac43\right) + \cdots [/math].

(Hint: Look at Problems Exercise and Exercise.)