Infinite geometric integral

Integral of 1/1+x+x^2+... from 0 to 1 using a geometric series. Is this integral easier than it looks? Watch this video and find out!

[vedhavarshini]

No one can dislike such a polite teacher like you sir. You make maths interesting and funny.

[ChronicleBlaster]

Indian flag because it was national maths day in India

Ramanunjan's Birthday

[seanfraser]

Because the geometric series doesn’t converge at x=1, the proper way to do the first integral would be to calculate the integral from 0 to b, and then take the limit as b tends to 1 from the left. You still get the same answer.

[nishatmunshi]

The way Dr Peyam finishes the video is very humble.

[dackid]

It is really interesting how adding/removing the number 1 can drastically change an integral

[lightdoingmaths]

Thanks a lot, very interesting as usual 👍

[stlemur]

Hi Peyam, I have found a formula for this integral for any whole number of terms in the geometric series. It turns out to always be the sum of an algebraic multiple of ln 2 and an algebraic multiple of pi! Let me know if you want to know more.

[umerfarooq]

Sir you always impress with your videos, you along with many other online teachers are contributing to changing lives for the better keep up the great work

[MohitSharma_calc]

For those who didn't understand how 1+x+x^2....=1/(1-x)
This is a simple way
Let f(x)=1+x+x^2....

=>f(x)=1+x(f(x))
=>f(x)-x(f(x))=1
=>f(x)=1/(1-x)
Voilá, you have it!
If this does help you leave a like below👇😊

Special thanks to Dr.Peyam (other youtubers such as bprp and flammable maths)who has really helped me learn calculus ...

[shivaudaiyar]

Thanks for such a great content with love from India

[dr.rahulgupta]

Excellent Integral and presentation both. Thanks with sincere regards DrRahul Rohtak Haryana India

[firozkhan_]

Great teaching sir! U made me learn something new today ☺️❤️

[mr.lawliet]

I like the way he says "alright thanks for watching" in the start. He is very calm and polite

[nanangmuhammad]

Oh mygod.. i dom think it... Excelent solution👏👏👏

[Mr_mechEngineer]

Exactly. I like how easy you make mathematics. I also like when you denote your name using pi and M

[michaelz]

You took the reciprocal of a divergent series, and then my head exploded. Thanks a lot.

[integralboi]

Are the Indian flag colours intentional?

[yograj_]

Love from India sir. I love watching your videos.

[ryanoftinellb]

As x approaches zero, 1 starts dwarfing x, x², x³…, so it fits intuition that the removal of the 1 might cause a big change to the integral.

[nanangmuhammad]

Is this convergen or divergen geometri series?