Add new comment

Disclaimer: I'm just a 7th grader who's smart, so don't trust me on this.

Alright, so there actually is a different proof that 1-1+1-1+1...=1/2. First, let's consider this way of solving this convergent series, namely 1+1/2+1/4+1/8.... We already know this sums to 2.

Let us call this series S. Then 2S=2+1+1/2+1/4+1/8... = 2+S.

2S=2+S
S=2

We can use similar methods to work with divergent series and other series. If 1-1+1-1+1-1... equals S, then S+S=1-1+1-1+1...+1-1+1-1+1-1...

Shift the second S over by one term, and all terms after the first in the first S get canceled out, leaving us with 2S=1 and S=0.5.

Similar methods are used in the final proof.

Filtered HTML

  • Web page addresses and email addresses turn into links automatically.
  • Allowed HTML tags: <a href hreflang> <em> <strong> <cite> <code> <ul type> <ol start type> <li> <dl> <dt> <dd>
  • Lines and paragraphs break automatically.
  • Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.