Example 4.15.  Show that    converges.

Explore Solution 4.15.

Enter the formula for the terms in the series.

  Use d'Alembert's ratio test. First, find the ratio of consecutive terms.

Since L < 1, the series converges.   

We can use Mathematica to find the sum of series.

Use Mathematica to construct some of the partial sums of the infinite series.

Use Mathematica to plot some of the partial sums of the infinite series.

We see that the infinite series    converges and that its sum is  .  

(c) 2006 John H. Mathews, Russell W. Howell