Question

SERIES, 3 MAJOR QUESTIONS (You may try to help me with whichever one you like):

MQ1:
http://i1084.photobucket.com/albums/j409/QRAWarrior/MATA36/MATA36-MQ1.png
(I do not understand what they are doing after the ">" sign)

MQ2:
http://i1084.photobucket.com/albums/j409/QRAWarrior/MATA36/MATA36-MQ2.png
(This does not make sense to me. Why can the series not approach 1 for instance as n-> infinity, and still be converging?)

MQ3:
http://i1084.photobucket.com/albums/j409/QRAWarrior/MATA36/MATA36-MQ3.png
(question is literally on the img)

Answer 1

@dpaInc

Answer 2

in the first example, pay attention to how they grouped the terms...

Answer 3

notice the 1/3 + 1/4 > 1/4+1/4 in S_4

Answer 4

i really don't like the way they proved it here.... can i show the way i'd group them? it's basically the same reasoning...

Answer 5

Yes for sure @dpaInc, please go ahead

Answer 6

notice the way they group the terms of the series....

Answer 7

since this is an infinite series, you can group the terms like this so that the sum is bigger than 1/2. and since you'll be adding 1/2 infinitely, this series diverge.