Write the first 5 terms of the sequence and find the limit of the sequence (if it exists).

Question

Assume n begins with 1.

a_n = 3/n {n+(2/n)[n(n-1)/2]}

If the limit does not exist , it would be helpful if you could explain why.

It would help a lot if you could show your work. Thanks!

Answer 1

I think you should be able to plug n=1, n=2 etc into the formula to get the terms.

You just need to be careful in the way you expand the parentheses.

a_n approaches 0 as n goes to ∞, because the numerator is fixed and the denominator approaches 2n² for large n, i.e. ∞.