conquer tricky sums with this nice trick

[@9WEAVER9]

I was already wearing my "good place to stop" tshirt today. Always nice to see what you're up to when I stop by your channel.

[@allanjmcpherson]

And it's a good thing you were! Otherwise we wouldn't have a good place to stop on this video.

[@t567698]

In the first example, setting x=2n+1, y=2n-1 also works: (x-y)/(1+xy) = 2/(1+(4n^2 - 1) = 1/(2n^2) arctan(1/(2n^2)) = arctan(2n+1) - arctan(2n-1). Using the claim we get in the limit "arctan(inf)" - arctan(1) = Pi/2 - Pi/4 = Pi/4.

[@CM63_France]

Hi, 16:06 : missing "and that's a good place to stop".

[@MortezaSabzian-db1sl]

Nice approach

[@r75shell]

and it's not best time to stop )

[@aadfg0]

What sets the claim apart from normal telescoping? Finding the right form to make a series telescope is the hard part. Recognizing you need to telescope may also be tricky, but the claim is no help for that.

[@maxl5423]

I don’t understand the Fibonacci one, fn+ 2 and fn seem like an + 2 and an , doesn’t that break the rule of an+1 and an ?

[@holyshit922]

This difference of arctans is not true for all x and y

[@xinpingdonohoe3978]

When is it different? When the two things are on different branches of arctan?

[@ivanlazaro7444]

​@@xinpingdonohoe3978 I think so

[@ethanbartiromo2888]

Only posted 22 minutes ago, nice

[@Alan-zf2tt]

fifth

[@suhaibalkhaldi]

first 😀

[@theguythatmakesyoumad3834]

Unsubscribed for participating in this members only nonsense...

[@Mystery_Biscuits]

?

[@theguythatmakesyoumad3834]

@@Mystery_Biscuits One of his other vids requires you to 'join'

[@2070user]

​@@theguythatmakesyoumad3834 Yes, but that's not really mandatory. Joining his membership and being a member allows you to watch videos EARLIER than those that aren't members. Michael Penn will still post the so-called "member-exclusive" videos later so you still get to watch them even if you haven't joined, the only thing is that you got to wait for some time. So in short, if you join the member, you get to watch the "member-exclusive" videos immediately. But if you don't join, you can still watch them after some waiting (usually days to within 2 weeks).