in number 7, Is the exponent of (-1) n right? I thought that the exponent of (-1) is n-1 because it changed from n=0 to n=1, and if (-1)^{n}, there will be a change of sign between negative sign and positive sign.

in number 7, Is the exponent of (-1) n right? I thought that the exponent of (-1) is n-1 because it changed from n=0 to n=1, and if (-1)^{n}, there will be a change of sign between negative sign and positive sign.

Question
Exponents and radicals
asked 2021-03-11
in number 7, Is the exponent of (-1) n right? I thought that the exponent of (-1) is n-1 because it changed from n=0 to n=1, and if \((-1)^{n}\), there will be a change of sign between negative sign and positive sign.

Answers (1)

2021-03-12
You are correct. It's easy enough to see if we just condense all of those extra factors into An's. Then the first expression gives \(\sum_{n=0}^\infty -1^{n})An = A0-A1+A2-A3+...\)
while the second gives
\(\sum_{n=0}^\infty -1^{n})An = A0-A1+A2-A3+...\)
where I converted An to An−1A because you can see that's what happened to all of the other factors in step 7
So that explanation has a mistake in it. If it's on Slader, be sure to leave a comment on that solution letting the person know.
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