Hello, SengNee!
This is neither an Arithmetic Series nor a Geometric Series.Given the series: .
show that the sum of the first terms of the series is: .
. . We must find another approach . . .
The denominators are "triangular numbers" ... of the form: .
We have: .
. . . . . . . . . .
. . . . . . . . . .
All the "middle" terms cancel out and we are left with:
. . . . .