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1. Draw a picture to show that $ \displaystyle \sum_{n = 2}^{\infty} \frac {1}{n^{1.3}} < \int^{\infty}_1 \frac {1}{x^{1.3}} dx $What can you conclude about the series?

Suppose $ f $ is a continuous positive decreasing function for $ x \ge 1 $ and $ a_n = f(n). $ By drawing a picture, rank the following three quantities in increasing order.

$ \int^6_1 f(x) dx \displaystyle \sum_{i = 1}^{5} a_i \displaystyle \sum_{i = 2}^6 a_i $

Use the Integral Test to determine whether the series is convergent or divergent.$ \displaystyle \sum_{n = 1}^{\infty} n^{-3} $

Use the Integral Test to determine whether the series is convergent or divergent.$ \displaystyle \sum_{n = 1}^{\infty} n^{-0.3} $

Use the Integral Test to determine whether the series is convergent or divergent.$ \displaystyle \sum_{n = 1}^{\infty} \frac {2}{5n - 1} $

Use the Integral Test to determine whether the series is convergent or divergent.$ \displaystyle \sum_{n = 1}^{\infty} \frac {1}{\left(3n - 1 \right)^34} $