Is there a infinite series that its limit goes to 0 however, it is increasing all the time? Or is there a infinite series that limit doesn't equal to 0 however, it is decreasing? (It is about theorm 5.1 for Calc 2) P.S. i don't think the (-) count..

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anonymous · Answer

Well, (-1)+1/2+1/4+1/8+... is increasing all the time but its limit goes to zero, so I guess there exists one!

anonymous · Answer

1/4 > 1/8

anonymous · Answer

the single terms are decreasing

anonymous · Answer

The series is increasing all the time... there's a difference between the sequence and the series.

anonymous · Answer

woops you are right, kind of got the wrong translation from german

anonymous · Answer

infinite series that is decreasing with limit not zero is fairly simple to find: for example, 3-1/2-1/4-1/8-... converges to 2 and is decreasing all the time.

anonymous · Answer

well but how this serious express as an equal? like Sn=..?

anonymous · Answer

because we are now on the alternating series