Question

Calc II Alternating Remainder Estimate Help Needed

Answer 1

Determine the smallest number of terms required to approximate the sum of the series with an error less than 0.0001.

\[\sum_{n}^{\infty}(-7^k)/(6^kk!)\]

Answer 2

I understand that you would set the sum equal to .0001 and solve for k. Right?

Answer 3

I can simplify the equation by saying (1/k!)x(7/6)^k right?

Answer 4

If I understood the problem correctly, there are a couple of ways to do it. Remember that the remainder estimate for alternating series is given by:\[|R_n| \le b_{n+1}\]So yeah, you can simplify it and put in the form:\[0,0001 \le \frac{7^{k+1}}{6^{k+1}(k+1)!} = \frac{1}{(k+1)!}*(\frac{7}{6})^{k+1}\]Or if you have a calculator, you can start expanding some terms until one of them is < 0.0001

Answer 5

I did that and I got to the seventh term, it was the right answer! Thanks! But on the test I won't be able to use a calculator, can this problem be solved some way w/o one?

Answer 6

If they ask for the smallest number, I guess you have to 1) manually compute the values or 2) solve an equation of the form above. If they do not, just pick a reasonable number and compute it, like n = 10. Very likely the error will be really small and it would suffice the boundary for |Rn|

Answer 7

And by the way, doing a series test without a calculator sucks a lot, huh

Answer 8

I agree with @bmp and add that you must fire your teacher.

Answer 9

Im not sure if we will be given this same type of problem but we did go over a problem like this in class that was WAY easier that we solved with very little effort

Answer 10

Why should one compute 7^k for k=1 to 7 and similar problems by hand. Those antiquated teachers should be trained to undersatand that the world has changed and they should follow the flow.