I'm having trouble interpreting anothher problem. There is a series
converges, is a series to which the limit comparison test applies with comparing series a p-series, and is a series to which the limit comparison test applies with comparing series with terms , i.e. , for some and with .
"If the series converges, give the limit within one percent. If the limit does not exist answer infinity, -infinity or DNE as appropriate"
Well, it is given that the series converges, but I don't understand what is being asked by finding the limit within one percent. Find the sum of the series or what? I don't understand how to find the sum of the series, either. If anyone has any ideas as to how I should approach this, I would greatly appreciate it.
Thanks for your help.
We have a rule of thumb that the error in truncating the series is of the same order as the first neglected term, so to find the number of terms needed we solve:
and round up to the next larger integer.
This is an approximate method rather than exact, but in this case is good enough.