I understand fully part a and b. But for part c they just plug in 1 , why is that? Why didnt they plug in 2 or 3 because those are between -5 and 5? Then how do they calculate the sum by plugging in 1? Thanks
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Hey minneola24. I think they are doing that in b) to answer c) since 1^anything = 1 for anything.
But then where do they get 5/16 as the sum?
They evaluated the derivative at x = 1 since the derivative and the power series are the same thing.
Ok, but I still dont see where they got the 5/16 from? How do you evaluate the derivative when x=1 and there is still another variable (n)
The n is a dummy variable for the power series: the function f'(x) has no other variables other than x.
Originally Posted by minneola24 Ok, but I still dont see where they got the 5/16 from? How do you evaluate the derivative when x=1 and there is still another variable (n) Ok. Then where is the 5/16 coming from? If anyone is understanding that part please enlighten me!
Originally Posted by minneola24 Ok. Then where is the 5/16 coming from? If anyone is understanding that part please enlighten me! You have so .
I'm confused where the 1/16 is coming tho!
Do the arithmetic! You have already shown that the derivative of is and, that by differentiating the power series for , . Setting x= 1 in both of those you get . Multiply both sides of that equation by 5.
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