Not Sure Why This Summation is equal to 1

[Matthewhistorian]

If anyone could explain that would be great

 

[blamocur]

Are you familiar with geometric series (https://en.wikipedia.org/wiki/Geometric_progression#Geometric_series)?

 

[Deleted member 4993]

If anyone could explain that would be great

Write out first 3- 4 terms of the series and see if you can find a pattern.

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[Matthewhistorian]

Are you familiar with geometric series (https://en.wikipedia.org/wiki/Geometric_progression#Geometric_series)?

Thanks this helps a lot, I wasn't familiar with it before I ran into this by adding powers of 2 in descending digit spots and got confused on why the pattern ended up being 1249999999... but now I see through simplifying how it ends up as 4/(5^n) which sums to 4/4 or 1. It's beautiful how math creates patterns like that sometimes.