Proving error bounds for ln 2 and sin x series

[emc92]

(1) Show that |ln 2 - Ʃ^N_n=1 ((-1)^n-1)(1/n)| ≤ 1/(N+1)
(2) Show that |sin x - Ʃ^N_n=0 ((-1)ⁿ)/(2n+1)!| ≤ |x|^2N+2/(2N+2)!


I really don't know where to start. should I change the sums to series first then work my way through? Please help!

 

[Dick]

Those are alternating series. The error bound is just the next element of the series.

 

[emc92]

ohhhhh wow now i see. thanks so much!