how to find the nth partial sum (arithmetic, geometric, telescoping)
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- เผยแพร่เมื่อ 30 มิ.ย. 2024
- How to find a formula for the nth partial sum of a sequence? A general strategy is to compute the first few partial sums and then look for a pattern. Also, remember we have the nth partial sum formula for arithmetic sequences and geometric sequences.
0:00 Q1 nth partial sum of an arithmetic sequence
5:29 Q2 nth partial sum of 1, -1, 1, -1, 1, -1, ...
8:47 Q3 nth partial sum of a geometric sequence
13:14 Q4 nth partial sum of a geometric sequence with a negative common ratio
16:39 Q5 telescoping partial sum
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One Calculus video a day keeps the nightmares away.
Lol yes
Lol it keeps the wrath of F grade away
You using the different colored markers interchangeably is actually really cool, thank you so much for the video, it helped a lot!
Thank you very much I was going insane in trying to figure out a formula for the nth partial sum of an alternating series
Thank you very much for this video!!!😭 It's been 3 days since I'm finding vids and websites where it can explain me how to find and divide (Sn) if there is no (n) given. And our teacher didn't taught us about it. SO THANK YOU VERY MUCH!!!❤❤
Q2:
Note: I used capital e (E) as capital sigma cuz it looks similar
E((-1)^i-1), i=1, n
= 1/2 x E((-1)^(i-1) + (-1)^(i-1)), i=1, n
= 1/2 x E((-1)^(i-1) - (-1)^i), i=1, n
(Telescoping series appeared)
=1/2 x ((-1)^(1-1) + (-1)^(n-1))
= (1+(-1)^(n-1))/2
9:14 That is really the quickest way
took me forever to realize the pokeball was a mic.
LOL..
yeah I give up. everyone's a genius at these, but I'm not lmao. i can't see patterns like others can i guess. I can hold fort in calc I and calc II until this chapter. so depressing.
Don't give up, wake up tomorrow and try again. You fail when you stop trying.
Humans are pretty well designed to recognize patterns, if you can't recognize them its very possible you've yet to see them enough to recognize them, so just keep at it and you very probably will recognize patterns better
I always skipped his video thinking he was speaking some Asian language lmao
now you know
nice