Infinite Limits & Infinite Series Mike Madro
Feb 21, 2016
Infinite Limits & Infinite Series
Infinite Limits & Infinite SeriesMike MadroInfinite LimitsIs a list or set of numbers written in definite order.T1/2, t2/3, t3/4, t4/5, ..., tn,In an infinite sequence each term has a successor As a sequence approaches a number such as 1 , we can say that the limit of the sequence is 1 Infinite SeriesIs the adding of an infinite amount of numbers In which we allow Sn to represent the sum of the terms in the series Ex. Sn= 0.5+0.25+0.125+0.0625As we add more terms to the series the sum gets closer to 1, therefore we can assume that the sum of the infinite series is 1If a series has a sum, it is called a convergent series. If not, it is called divergent.
Real WorldZenos second paradox involves a race between the Greek hero Achilles and a tortoise. In this problem Zeno argues that at Achilles start position a1 and the tortoise start position t1, when Achilles reaches point a2=t1 the tortoise will be ahead at position t2. Therefore, at position a3=t2 the tortoise will still be ahead at t3. This process should continue indefinitely.
Real World Infinite SeriesIn another of Zenos paradoxes: a man is not able to walk into a wall because he would always be going half the distance. This halving of distance would continue indefinitely.
5How to learn infinite limitsSub positive integers into the place of nDetermine what the limit approaches
How to learn infinite seriesSub positive integers into the place of nAdd up the series
=2Questions State the limits of the following sequence, or state that the limit does not exist.1/3, 1/9, 1/27, 1/81, 1/243, , (1/3)2. 1, 2, 3, 4, 5, , n,
nFind the following limit or state the limit does not exist.3)
LimLimDetermine whether the following series converges or diverges
LimFind the sum of the following series or state that the series is divergent.6) 1+ 1/3 + 1/9 + 1/27 + 7) 1 2 + 4 8 + 8)9)