Q:

Would the sum of an infinite series be finite if there were gaps between each numbers that increased until reaching infinity?

If you were to have a series:
1+1+2+4+7+11+16+22...
Where the gap between the numbers increased by one every time, wouldn't this gap eventually become infinite? Once it was, what would happen? Would it be possible to sum this series because although it is infinite, it has the infinite gap as well, so would this infinite gap stop the infinite series? And if it did, would the infinite series even be considered infinite, although it would have to be infinite in order for the gap to reach infinity.

A:

No. At any point the gap is finite. The gap will never become infinite.

