Bounding values for partial sums of alternating series.

Question

inkyvoyd · Answer

So, here I have a 4 part question with the last 3 parts about alternating series. I can't figure out iv.

Should've paid more attention in my "online class" >.>

inkyvoyd · Answer

ps I know the answer but I have no idea how to "justify" it.

inkyvoyd · Answer

@Hero , @phi , @Mertsj , any ideas what parts I'm missing?

inkyvoyd · Answer

To clarify, I just showed that an alternating series converges - but how do I tell whether the partial sum is above or below the actual value?

mertsj · Answer

You need one of the smart guys.

phi · Answer

I assume $M_{10}$ means you sum from n=1 to 10 ?
if so , the last term has -1^11  or -1
the next "correction term" after this is +.  so it seems that the M10 sum is too small

inkyvoyd · Answer

Ah - so for all alternating series, I can look at the (-1)^n and tell if the sum is to big or small?

phi · Answer

yes.  the sum is alternating above and below the value it is converging to

inkyvoyd · Answer

oh jeez - so intuitively alternating series are called alternating because they both alternate in sign, and because they go above and below the sum S...