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$$\left(\sum_{j=0}^n x_j\right) + x_{n+1} = \left(\sum_{j=0}^{n-1} x_j\right)$$

It's not obvious to me that the two are equal. It seems that the left side goes up to $n + 1$ whereas the right side goes up to $n - 1$.

Toby Bartels
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Andrew
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    You're right... they are only equal when $x_n+x_{n+1}=0$ – TheBestMagician Jan 06 '22 at 20:04
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    @Andrew Where does this question come from? It is likely that either you copied it incorrectly or that the original has a typo. – Ben Grossmann Jan 06 '22 at 20:07
  • @BenGrossmann I am pretty sure I copied it correctly, so perhaps the typo is in the text.

    This is from page 59 in Fundamental Methods of Mathematical Economics 4e. You can find the pdf here --> https://www.academia.edu/31668030/Fundamental_Methods_of_Mathematical_Economics_Fourth_Edition_Alpha_C_Chiang_Kevin_Wainwright

     – Andrew Jan 06 '22 at 20:17
  • I downloaded the PDF, and it's pretty fuzzy; there appears to be a bump on the minus sign in the upper limit $n-1$, so my guess is that it's really $n+1$ but the scan is so bad that it looks like $n-1$ instead. – Toby Bartels Jan 06 '22 at 20:20
  • @TobyBartels thanks I guess I missed that. Now the question is quite obvious. Thanks for your help on this! – Andrew Jan 06 '22 at 20:29

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