Following up on TheEmptySet's post.
back substitute and
This result is called as "telescoping sum."
on that new way you showed me how would i get the sum?
i stick values for n of 0, 1, 2, 3... and see if there is number not reapeating?
but for the new method seems more understandable
i put n = 1 and got -1/30 which aint the sum:?
It's n=1 in :)
but you said
(-1/n+4) + (1/n+5)
why dont you add?
Because 1/(n+5) annulates with the following term, and so on...
Just write the few first terms of the series on a paper, and you will see that..