Math Help - Finite sum?

I am doing some problems in sigma notation and two of them have come up with an ERR: INVALID DIM on my calculator screen, the problems were as follows: lower limit = 1, upper limit 1000 and index of summation 1/n, the other one had lower limit = 1 and upper limit = 5000 and index of summation 1/n. Are these sums considered finite? Why?
Thank you,
Keith Stevens

Originally Posted by kcsteven

I am doing some problems in sigma notation and two of them have come up with an ERR: INVALID DIM on my calculator screen, the problems were as follows: lower limit = 1, upper limit 1000 and index of summation 1/n, the other one had lower limit = 1 and upper limit = 5000 and index of summation 1/n. Are these sums considered finite? Why?
Thank you,
Keith Stevens

I think you are misusing some terminology? You are looking for the sum of 1/n as n goes from 1 to 1000 for your first question, yes? Otherwise I can't make sense of it. (The index of summation here is "n", not 1/n. The 1/n would be called the "summand," I believe.)

Both of these are necessarily finite since we are taking the finite sum of a set of finite numbers. However both of these sums will take a while for your calculator to compute, particularly if you try to do them in "exact" mode.

I get 7.48547 for the first sum and 9.09451 for the second, which shows just how slowly this series diverges.

-Dan