Partial sums intro | Series | AP Calculus BC | Khan Academy

[@josipgavran]

I love this guy: ''If someone were to walk up to you on street and say -Okay, now that you know notation for a partial sum... ''

[@JimisekMichalas]

Keep Calm and love Khan.

[@tinay_reads]

How do you know what the SsubN is based on the Series? 😅 Or is it just actually given when solving the problem?

[@UltimateBargains]

Is there a general way to derive the partial sum formula from an infinite sigma notation (assuming that the infinite series is convergent)?

[@mj6637]

from my understanding, the partial sum would just be the integration of the original function up to the nth term, or the area under the curve of the original function for those n terms. If the original function is a constant (therefore whose derivative is zero) it would equate to a simple adding of n terms, its quite easy as its area is equates to the base times the height of a rectangle or square, or whose underlying integration is just n times its height which is constant; for a linear function whose derivative is constant, its integration would amount to a triangle whose area is 1/2 base times its height; for a quadratic function its derivative is a linear function, whereas its area or integration is a cube and so on and so forth...

[@adityaadit2004]

So partial sum is just a shortcut to do a sum? (Like, converting a sigma notation that has variable i in it and an upper boundary of n to some formula that no longer requires the i variable and uses n variable instead?)

[@freebird889]

Ssub6 if it is adding all the terms is equal to 102515/255936. Please explain why you only used the last one as in Ssub6????????????????????

[@isavenewspapers8890]

No, that's what would happen if a-sub-n were equal to (n^2-3)/(n^3+4). However, (n^2-3)/(n^3+4) is actually what S-sub-n is equal to.

[@joshiifruit5554]

you are the best truly

[@dushsam]

what an interactive explanation 😂. Everything make sense now 😉

[@Queen-uw7ww]

like others if you are going ro find a partial sum you are supposed to add a sub 1 - a sub 6 but you just computed the S sub 6??

[@EmpyreanLightASMR]

3:00 let's just pull that out of thin air. I hate that I don't get any of this

[@lilhypersee6832]

How did you get s6

[@shivibaby97]

Can you tell how we can say this series cgs to a number meaning finding that number This question asked many time

[@Ibrahmoment]

I guess I'm too late but still if you meant this series, 2:48, then we are given the nth term of the sequence of partial sums, find lim n→∞ S_n which is 1 hence the series converges to 1

[@freebird889]

This makes no sense. If you're adding a1+a2+a3+a4+a5+a6 then why do you only calculate a6????????????????????????????????????????????????????????????????????????????????????????????????????

[@isavenewspapers8890]

Why did you type so many question marks?

[@asjednazir6582]

Sal no one on the street ask us these questions

[@DiannaMarieMacabane]

PANOO PO NAGING 49/36?

[@light8174]

This didn’t help at all Sal.

[@ian.ambrose]

Too bad lol

[@sabitaraniraiguru1628]

Bro, it could be reduced to 3/20, just divide by 11.

[@NiteSaiya]

The sum of the first 6 terms cannot be equal to the 6th term alone. What the hell is this?

[@santoryu8940]

is this true?

[@vascubalee]

Faux Mustache misunderstood the video. S(n) is not the same formula as a(n). S(n) = the SUM of a(n-5) + a(n-4) ... + a(n). So you could use the formula for a(n), plug in each n and solve, and add up the 6 answers. Or you could find a formula for S(n) and only have to plug in one value for n and solve. The way you derive the formula for S(n) is similar to how you derive the formula for a(n), but they are not the same formulas.

[@santhosh7658]

@@vascubalee how to derive formula of S(n)?