What is the equation for this pattern?

Question

I really should be able to nail down an equation for this sequence, but my mind has completely deserted me regarding how to represent it in equation form. 1, 1.5, 1.75, 1.875, 1.9375, and so onwards. Effectively +0.5, +0.25, +0.125, +0.0625 and so onwards.

Thanks for your help guys. :)

Update:

That's perfect Ian, thanks a lot. :)

I assume that the sum to infinity would therefore be 2?

Thanks for your help guys. :)

? · Accepted Answer

1, 1.5, 1.75, 1.875, 1.9375,
As you correctly observed, the differences are
1/2, 1/4, 1/8, 1/16

Written in improper fraction form the original terms are
1, 3/2, 7/4, 15/8, 31/16
Hopefully you will find it easy to see that the denominators are powers of 2.
The denominator for the nth term is 2^(n - 1)

Try to see the pattern with the numerator now.
If the denominator is d, the numerator is 2d - 1

The nth term is (2^n - 1)/2^(n - 1)

Is that what you needed? You did not mention summing the series.

Regards - Ian

What is the equation for this pattern?

1 Answer