Practice Series in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The result of adding all the terms of a sequence together, either finitely or infinitely many terms.
Add up all the terms: a_1 + a_2 + a_3 + \ldots — an infinite series can still have a finite sum if terms shrink fast enough.
Example 1
easyCompute partial sums S_1 through S_4 for \sum_{n=1}^{\infty} \frac{1}{2^n} and identify the limit.
Example 2
hardShow that the harmonic series \sum_{n=1}^{\infty} \frac{1}{n} diverges.
Example 3
easyWrite the first four partial sums of 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \cdots
Example 4
mediumUse the divergence test on \sum_{n=1}^{\infty} \frac{n}{2n+1}.