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I am suppose to separate the last term of the given sequence.

$$\sum_{j=0}^n2^j$$

my work as shown... $$ \sum_{j=0}^{n-1}2^j\ +\ 2^n$$
Does this appear wrong?

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  • $\begingroup$ Yes, this is just the definition of the sum symbol. For $n=2$, for example, $\sum_{j=0}^ 2 2^j=2^0+2^1+2^2=\sum_{j=0}^1 2^j+2^2$. Here $n-1=1$. $\endgroup$ – Dietrich Burde Apr 16 at 14:55
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    $\begingroup$ This appears correct to me. To make it clear the $+2^n$ is not inside the sum, you might want to place parentheses around the sum, as in: $$\left(\sum_{j=0}^{n-1}2^j\right)+2^n$$ $\endgroup$ – Clayton Apr 16 at 15:01
  • $\begingroup$ No, it does not appear wrong $\endgroup$ – J. W. Tanner Apr 16 at 15:01
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    $\begingroup$ I'd even add to @Clayton's idea, that you might separate out that "last term" in front, so you write $$2^n + \sum_{j=0}^{n-1} 2^j,$$ at which point the parentheses are unnecessary. (This doesn't work quite so nicely when you have to pull out the first and last terms, and it's natural to place those before and after the main sum, but it's still not a bad practice.) $\endgroup$ – John Hughes Apr 16 at 15:07

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