Question

Determine whether the following series converges or diverges. Say what comparison test you usied and what series you used for comparison: Σ_{n=3}[infinity] {1}√{n-2}

Answer 1

The given series diverges.

Step-by-step explanation:

In order to determine whether the series ∑n=3∞ 1⁄√(n-2) converges or diverges, we can use the comparison test.

We can compare this series to the harmonic series, ∑n=1∞ 1/n, which is a well-known divergent series.

By comparing the terms of the given series to the terms of the harmonic series, we can see that for all n ≥ 3, ¹⁄√(n-2) ≥ 1/n. Since the harmonic series diverges, the given series also diverges.