Solved Problems for Series: Summing Them Up

Here we will show basic approaches to summing up and approximating series.
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• Problem: Find the sum of the series

  

• Problem: Find the sum of the series

  

• Problem: Find the sum of the series

  

• Problem: Find the sum of the series

  

• Problem: Find the sum of the series

  

• Problem: Approximate the sum of the series

  

  by its partial sum s₂₀ and estimate the error of this approximation.

• Problem: Approximate the sum of the series

  

  by its partial sum s₁₀₀ and estimate the error of this approximation.

• Problem: A certain rubber ball when dropped on a hard floor bounces back up to the 3/4 of the height from which it was dropped. We decide to ignore effects of elasticity and small-scale phenomena. Find the distance that the ball travels if it is dropped from the height of 2 meters.