Can anybody help me with this question
#Infinite series
young herald
did you try to use the ratio test?
hidden timber
;
Don't believe I've learned that yet. The tests we've learned are nth term, geometric series, telescoping, p series, and integral test
The problem should be solvable using just those
young herald
ah okay, also looks like the ratio test doesn't even work lol
hidden timber
I have a picture of the answer key, though I can't understand that either
young herald
could you send me it?
hidden timber
hidden timber
Yes
young herald
what they did was rewrite the series such that each term of the series is greater than each corresponding term of the harmonic series
well half of the harmonic series anyways but that diverges also
does that make sense? my wording might be a little scuffed lol
hidden timber
How exactly did they re write it? I guess that's what I'm confused about
For example in line 2, why is the 1/2n factored out?
young herald
they shifted everything over by one
kind of like telescoping series?
if you try to match each term from the numerator to the corresponding term on the denominator
the second numerator term matches with the first denominator
the third numerator with the second denominator
etc
hidden timber
What is the point of that?
young herald
until you get to the nth denominator term, which has nothing to match with
uhh
you know telescoping series
it's like
hidden timber
Yeah ik what telescoping is
hidden timber
Where is stuff canceling though?
hidden timber
Where is the stream?