1. ## Series True/False prob

How would I go about proving these statements true or false?

"If a series is truncated after the nth term, then the error is less than the first omitted them"

"If r<1, then the series E r^n converges"

2. Originally Posted by Nerd
How would I go about proving these statements true or false?

"If a series is truncated after the nth term, then the error is less than the first omitted them"
No. (I might not be understanding you correctly.
"If r<1, then the series E r^n converges"

3. Originally Posted by ThePerfectHacker
No. (I might not be understanding you correctly.
I'm not quite sure what you're trying to say either, but that's what my homework is asking me. True/False. It sounds familiar, but not enough for me to be confident about an answer and guessing is useless, won't help me learn, and won't get me credit (ALL work must be shown)

Originally Posted by ThePerfectHacker
Oh...right. -1. Not that hard a number to thunk up...And I've seen that example over a dozen times. Sometimes, it's the obvious that elludes me the most.

4. [quote=Nerd;47830]How would I go about proving these statements true or false?

"If a series is truncated after the nth term, then the error is less than the first omitted them"
quote]

False. Consider the series:

S=1 + 2 + 3 + 5 + 0 + .. + 0 + .. = 11

S(1) = 1

(where S(n) is the sum of the series truncated to the first n terms)

The first omited term is 2, but the error is 10.

RonL

5. Originally Posted by Nerd
"If r<1, then the series E r^n converges"
False, as ImPerfectHacker tries to point out r negative but |r|>=1 gives
a series which does not converge, but with r<1.

RonL