shamieh
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Determine whether the following series converge or diverge. You may use any appropriate test provided you explain your answer.
$$\sum^{\infty}_{n = 1} (\frac{1}{\sqrt{n}} - \frac{1}{\sqrt{n + 1}})$$
So it looks like this problem wants me to do telescoping series or something of that nature but I really want to avoid writing out those terms, can't I just split this into two sums and say this:
$$\sum^{\infty}_{n = 1} \frac{1}{\sqrt{n}} - \sum^{\infty}_{n = 1}\frac{1}{\sqrt{n + 1}}$$
Evaluating both of the series using p series test since, p $$\le$$ 1 for both series then the whole series diverges?
Is this correct?
$$\sum^{\infty}_{n = 1} (\frac{1}{\sqrt{n}} - \frac{1}{\sqrt{n + 1}})$$
So it looks like this problem wants me to do telescoping series or something of that nature but I really want to avoid writing out those terms, can't I just split this into two sums and say this:
$$\sum^{\infty}_{n = 1} \frac{1}{\sqrt{n}} - \sum^{\infty}_{n = 1}\frac{1}{\sqrt{n + 1}}$$
Evaluating both of the series using p series test since, p $$\le$$ 1 for both series then the whole series diverges?
Is this correct?