You are Here: Home >< Maths

# Geometric Series watch

1. What if ????

For what values of M and N does this formula hold? Can they both be negative? Does N need to be greater than M?
2. If then for each value of , so your sum is . You just have to work out how many 1s you're adding together.

And to work out what values of M and N it holds for, think about how the formula is derived.

We can fix and for each write . Then:

and so:

You can take one of these away from the other (so loads of terms on the RHS cancel, leaving just two). Rearranging gives you the formula you have. Does this place any condition on M,N? I'll let you decide that for yourself.

[EDIT: Just to clarify a point, if then by definition the sum is zero (e.g. if you're summing the integers from 3 "up to" 1 it doesn't make much sense).]

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: September 29, 2010
Today on TSR

### Summer Bucket List is Back!

Start yours and you could win £150!

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams