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    I can't rearrange, it seems. Anywho, fixed.
    OCR C1/C2 book, p342 Ex 6B
    Find the sum of the following geometric series:
    1+\frac{1}{2}+\frac{1}{4}+......  +\frac{1}{2^n}
    So I tried it, using ari-1 to find the ith term and ended up with \frac{1}{2^i^-^1}=\frac{1}{2^n} and i-1=n therefore i=n+1. I then put it into the formula: \frac{(\frac{1}{2})^n^+^1 -1}{-\frac{1}{2}} and rearranged to get 2-\frac{1}{2^n^+^1} ...which is wrong. The book gives 2-\frac{1}{2^n}, implying that the ith term is n.

    I had the same problem with the next two questions - where am I going wrong? Why is the ith term n and not n+1 with these? Thanks.
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    (Original post by Contrad!ction.)
    OCR C1/C2 book, p342 Ex 6B

    So I tried it, using ari-1 to find the ith term and ended up with \frac{1}{2^i^-^1}=\frac{1}{2^n} and i-1=n therefore i=n+1. I then put it into the formula: \frac{(\frac{1}{2})^n^+^1 -1}{-\frac{1}{2}} and rearranged to get 2-\frac{1}{2^n^+^1} ...which is wrong. The book gives 2-\frac{1}{2^n}, implying that the ith term is n.

    I had the same problem with the next two questions - where am I going wrong? Why is the ith term n and not n+1 with these? Thanks.
    I won't comment on what you're saying about the ith term, as I'm not clear what you mean.

    However, your initial formula is correct; you're going wrong when you re-arrange it.

    \frac{(\frac{1}{2})^n^+^1 -1}{-\frac{1}{2}}

    =2- \frac{(\frac{1}{2})^n^+^1}{\frac  {1}{2}}

    =2- (\frac{1}{2})^n

    =2- \frac{1}{2^n}
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    (Original post by ghostwalker)
    I won't comment on what you're saying about the ith term, as I'm not clear what you mean.

    However, your initial formula is correct; you're going wrong when you re-arrange it.

    \frac{(\frac{1}{2})^n^+^1 -1}{-\frac{1}{2}}

    =2- \frac{(\frac{1}{2})^n^+^1}{\frac  {1}{2}}

    =2- (\frac{1}{2})^n

    =2- \frac{1}{2^n}
    *facepalm* Thanks, I now feel like a pillock

    As soon as I saw the halfn+1 over a half, it clicked. I think I was just laying it out awkwardly so that I couldn't see where I was going. Oopsie.

    Merci buckets.
 
 
 
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