# Proof by Induction - Example 1

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• Published on Aug 3, 2010
• Thanks to all of you who support me on Patreon. You da real mvps! \$1 per month helps!! :) www.patreon.com/patrickjmt !! Proof by Induction - Example 1

## Comments • 576

• syed saba 4 days ago

Amazing.. Video ðŸ‘ŒðŸ‘ŒðŸ‘ŒðŸ‘Œ

• Inayat khan 6 days ago

perfect

• Garen Kantarci 7 days ago

Has anyone told you that you are a god among men?

• mqhele mguni 22 days ago

2019 at PJMT BUSE University says Patrick is the TRUTH!

• Simi S 28 days ago +1

Anyone noticed that he is left hand ed

• Greggie Pattry 2 months ago

do i always assume the statement is true?

• Lars K Month ago

You assume the statement is true. For any natural number k the statement works. So IF the thing you assumed is true, then the statement also works for k+1. Therefore, since you have already proven that k=1 works, your assumption is correct. And therefore you can conclude the statement works for 2, 3, 4...
Assuming that the statement is true is vital in this case.

• Thifal Raniah 2 months ago

Thank you so much! ðŸ”¥ðŸ’›

• Sunil nair 2 months ago +1

Tnx sirðŸ˜ŠðŸ˜Š

• Josh Lipovetsky 2 months ago

Thank you!

• stellus francis 3 months ago

Thnx a lot.......

• Helen Jay 3 months ago

Thank you very much for this video I'm doing my maths exam revision now.

• arletd paucar 4 months ago

wow I didn't get it until I saw your video! very helpful

• Frank V 4 months ago

Halfway through the video and all I keep thinking is, "So this is what people have to deal with watching me write something left-handed? My hand covering up what I'm writing until I'm done?"

• Sebastian Suarez 4 months ago

Why do you add 5(k+1)-1 to the left side and not just 5(k+1)??

• Helen Jay 3 months ago +1

The K plus 1 was shoved into the equation.

• Elvin Gamers 4 months ago +1

Hello 2010

• Stephen Mack 4 months ago +2

Your videos on induction, partial fraction decomposition, and derivatives are saving my life before finals rn tysm

• Landon Shenberger 6 months ago

THANK YOU

• Divya Shukla 6 months ago

G

• PicledH 6 months ago

what is the additional term for??

• Queso Dilla 6 months ago

Too bad this would get me marked in my class as my teacher counts 0 as a natural number which disproves the base case lol

• crissy newton hwaaa 6 months ago

this is simply the best keep on keeping on

• Fade 6 months ago

Goddamn, I should've watched this video instead of rereading the same section from the textbook for hours.

• Sam Saghafi 7 months ago

You have literally taught me in 6 min what I have spent up to 10 hours learning from my professor, textbook, quizzes, and assignments. You r the best TheXvid tutor. Thank you

• Nigel Sterne 7 months ago

Ive been searching for hours and this is the only vid that made sense, thanks!

• Chuyu Liu 7 months ago

Thank you

• Joseph G. Hotto 9 months ago

*breathes a sigh of relief*

• Victor Tsenov 10 months ago

thank you kind sir.

• ToXiiC NebuLa 10 months ago

Lol, this may seem weird but I find it satisfying to watch and learn from Left-handed mathematicians. Their hand usually is in the way of some of the problem whilst writing it out, therefore, it gives me the logical reason of being last to answer for being the only one to go back and read the problem once more. â˜º

• Xylok 10 months ago

i bet i can become three times better at math than you before you can eat and transform into nothingness a full size universe!

• Xylok 10 months ago

18 seconds in; got some glimpse of some of the hint of the gist of the depth; laughed hard, kept watching on, finished the vid, wrote this comment, went on with my mediocre hair day to ongoing presents.

• ORACLE OFFICIAL 10 months ago

i'll teach you to be right handed cz your left hand really really really sucks..!

• aeroO bics 11 months ago +1

Induction must be the least elegant type of proof. We are assuming to much. And of course the result will end up correct. P(m) + X will always add up to P(m+1)

• n n 11 months ago

Wow couldn't be any easier

• Eric Meyerhuber Year ago

Nice clear example and explanation. I knew it wasn't hard, but the book and prof did not do what you did. Thank you very much.

• Meg Anedez Year ago

Pls answer me why thereâ€™s additional i dont get it

• Antonio J G-B Year ago

Patrick I'm sure you get a lot comments praising you so instead just get yourself an ice cream for your well put explanation on the concept of proof by induction.

• Antonio J G-B Year ago

I'm confused as to why he went from 4+9+14+19+...+(5k-1) into (k/2)(3+5k)

• Antonio J G-B Year ago

I figured it out, he replaced it because we substituted with the P(k) expression from our assumption.

• THE ROYALS Year ago +2

sir where is 13k coming from and why

• Nemisha Chris Year ago

Why we adding additional term in left hand side

• Karabo Monaiwa Year ago

Yet you save my life again...

• I dont get it. Sorry for my stupidity

• Twisting Tiger Year ago

I wish he wasn't left-handed. His left hand acted as a barrier ðŸ˜•

• patrickJMT  Year ago

yea, it does get in the way sometimes. i try to be conscious of it but often forget

• Dexter Nicer Year ago

where did you get the times 2 in 4k/1?

• Ahmed Mirza Year ago

Where is 5k gone plzz tell me

• Yousif Sirrieh Year ago

mnwer ya gale

• Darknavy42 Year ago

Exam is in 30 minutes and yet again, I learn more from you. Cheers

• Aimee W. Year ago

just want to let you know that I'm in love with you.

• Blo op Year ago

Deyam

• Warren Binder Year ago

8 years later, thank you!

• Robert Wagner Year ago

Good stuff

• Chandru .A Year ago

We should write in your right hand

• sophie ng seah Year ago

useful video! Thumbs up!

• My discrete math assignment thanks you

• Pedro Torchio Year ago

Naturals bigger than zero, right? Or are you considering Natural numbers as positive Integers? Thanks for the vid

• whenever im searching a topic on maths i include Patrick at the end just for em to take me straight to ya, ya are the best. thank ya

• Jack Daniel Year ago

Damn, your writing is so clear and fast!

• James 2: 6-7 But you have dishonored the poor. Is it not the rich who are exploiting you? Are they not the ones who are dragging you into court? Are they not the ones who are blaspheming the noble name of him to whom you belong?

• Caspar Claessen Year ago

Thanks a lot because of you I have courage and hope that I will pass my exam tomorrow

• Kameryn Cherry Year ago +13

math makes me want to die. Your explanations make me want to die less. thanks lol

• Thanks!