For a series with the sum from n=0 to infinity, when the sums start off positive do you use (-1)^n or (-1)^(n+1)?
When finding Taylor coefficients, if the signs alternate with the first derivative as positive, which do you use for the expression for the nth derivative???
When finding Taylor coefficients, if the signs alternate with the first derivative as positive, which do you use for the expression for the nth derivative???
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"For a series with the sum from n=0 to infinity, when the sums start off positive do you use (-1)^n or (-1)^(n+1)?"
Plug in the index of the first positive term, usually either 0 or 1, and see which yields a positive term, (-1)^n or (-1)^(n+1)
If the index of the first positive term is 0, then (-1)^n = (-1)^0 is positive
If the index of the first positive term is 1, then (-1)^(n+1) = (-1)^(1+1) is positive.
"When finding Taylor coefficients, if the signs alternate with the first derivative as positive, which do you use for the expression for the nth derivative???"
Same answer as above, use the one that gives a positive result when you plug in the index of the first positive term.
Plug in the index of the first positive term, usually either 0 or 1, and see which yields a positive term, (-1)^n or (-1)^(n+1)
If the index of the first positive term is 0, then (-1)^n = (-1)^0 is positive
If the index of the first positive term is 1, then (-1)^(n+1) = (-1)^(1+1) is positive.
"When finding Taylor coefficients, if the signs alternate with the first derivative as positive, which do you use for the expression for the nth derivative???"
Same answer as above, use the one that gives a positive result when you plug in the index of the first positive term.
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(-1)^n is positive when n=0