Can You Find the Sum of the Infinite Series? | Learn How!

#OlympiadMathematics #OlympiadPreparation #CollegeEntranceExam

[silviatotaro]

Cheers and compliments from Italy! Here, in Italy the series is called Mengoli series, after the mathematician Pietro Mengoli ( 1626 – 1686). It is the first example we make to introduce the concept of series. I did it plenty times, when I taught mathematics at the university.

[thomaskeating]

Pease don't stop with these videos. So insightful. We need more of this enlightenment, and you make it so clear, ---well. it's clear you aren't paid enough because you probably deserve a lot more.

[marioperic]

Excellent professor. Without developing into infinity order, the task can be solved more shortly. It is known that the sum can be divided into two sums: SUM n=1, inf(1/n) - SUM n=1, inf(1/(n+1)). First sum can presented as: 1/1+SUMn=2, inf(1/n). If we introduce a replacement m=n-1 it goes: 1+SUM m=1, inf(1/(m+1)) - SUM n=1, inf(1/(n+1)). Since for the summing, it is irrelevant what is the tag n (n, or m, or x) if the structure is the same the sums are actually the same. So the final result is 1!

[kafaichan]

1/n(n+1) = [1/n - 1/(n+1)], summation to infinity of all terms = only with 1st term & last term [1- 1/(n+1)], n-> infinity implies last term = 0, so ans = 1

[AntonioSaracino]

brilliant and thoroughly explained; thank you so much

[JD_ALMIGHTY]

It's about drive
It's about power
We stay hungry
We devour
Put in the work
Put in the hours
And take what's ours

[math]

excellent demonstration showcasing how to find the sum of an infinite series, thanks for sharing

[mahalakshmiganapathy]

I never miss your class .i like your explanation very much

[furzaanullah]

That's looking nice. I enjoyed solving it.

[holery]

Just apply the partial fraction on 1/n(n+1). So that, 1/n - 1/(n+1). If you see this form, there's will be cancel each other. Thus the answer is must be 1

[wackojacko]

I'm thinking not all infinities are the same. Thank you for posting. 🙂

[lavc]

Dear teacher, thank you for starting series .

[chandankumargupta]

This type of series is named as telescoping series, which is I study in bsc

[gudyou-atul]

Sir i have a question ❓ x^2+x^2+x^4. Find the number of polynomials

[r.a.]

Ahhhh.... partial fraction, I learned integration by partial fraction.

[albertomarin]

Una solución mejor: esa fracción es la resta de 1/n - 1/(n+1), si desarolla el primer término de 1/n da 1 y el resto empezando en 2 y la resta intacta, luego la suma que empieza en 2 la pone a iniciar en 1 y suma 1 al índice n entonces se anula con la resta y el resultado es 1