For (c), I know that the definition of a Cauchy sequence is when the terms eventually become really close. I can see that the terms are becoming closer and closer to each other but does this sequence actually converge?
Thanks
2026-04-02 17:29:05.1775150945
Is this sequence with a square root in the denominator a Cauchy sequence?
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By b), you have $$\lvert a_{n+p}-a_n\rvert>\frac p{\sqrt{n+p}}\ge \frac p{\sqrt{2p}}=\sqrt{\dfrac p2},$$ which tends to $\infty$.