Sum of the series of partial sums (KristaKingMath)

Learn how to find the sum of the series using its corresponding series of partial sums. Understand the difference between a series and a series of partial sums, and then use the fact that the sum of an infinite series is equal to the limit as n goes to infinity of the series of partial sums to the find the sum of the infinite series.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[alexvu]

I got a test in about 48 hours, last min notification for the test by the prof. and your videos are saving my life rn. Thank You

[rubendarioanguloquemba]

I want to be a master in mathematics, and all your videos really help me to achieve that goal. Thanks, and I want to take all your classes, maybe takes more than one year but eventually I'm going to achieved it. Thanks for be a great teacher.

[osohexxy]

Thank you for making a straight forward video not filled with off topic information that actually teaches you in a fairly simple way.

[instaminox]

the best video on youtube regarding partial sums

[turbocrackers]

Omg you're incredible. I was looking for a tutorial on a problem almost exactly like this and you helped so much!

[hg.]

Sorry not to catch on like the rest of the commenters here, but i could have used a "tabling out" of the actual "a" so I can see in tabular form where the "infinite sum" of a's is going. And yes, I could do that myself, but Krista has spoiled us with how "easy" (more like 'convenient') she makes this for the rest of us.

[timeonly]

I think when you said "the *series* of partial sums" you meant the **sequence** of partial sums.

Those are two *VERY* different things.

[mibraribrar]

Brillient mam, I was founding like this and yes it does

[ronraisch]

the sum of the series of partial sums is taking the sum over all n of Sn which is infinity, and NOT just doing the 2 sec calculation that this series of Sn approaches 2 when n approaches infinity

[drakefire]

This is incorrect. The limit of the partial sum DOES NOT ALWAYS EQUAL the Series Sum. That's only if it's certain types like Geometric. That example is a divergent series without any finite sum. I've been searching this topic and found numerous online videos and colleges make the same mistake.

[WilliamBlake-yjyu]

So we basically assume the digit goes to zero when the value continues to decrease each time we increase the value of the exponent?

[DrivingVideosSSH]

where are you getting the terms for the A sub n???