1) 

a) Plot a hundred terms of the sequence a[n] = (-1)^n*sin(1/n)  and guess its limit by looking at the plot.  (It almost looks like we have 2 sequences in our plot.  The -1^n term makes the terms oscillate between positive and negative values, i.e. values above and below the x-axis.)  Then evaluate the limit using Maple.   

b) Consider the series . Plot the sequence of terms and the sequence of partial sums on the same graph.  (Plot 50 of each; use the display command for this, and also use different 'symbol' values in your plot commands so you can see which plots are which.)  Then evaluate the sum using Maple.  Since the series converges, the terms must go to zero, and that's what we saw in the plot.  (The value of this series is a famous result due to Euler.)