#17 proof prove induction 8^n-1 is divisible by 7 divides mathgotserved induccion

Показать описание

Prove

Math Tutorials Links
Algebra
Foundations

Equations

Inequalities
Solve Systems of Equations by Graphing

TESTS

Рекомендации по теме

Комментарии

Why not use the following for the induction step? Assume by induction hypothesis that 8^n - 1 is divisible by 7. We need to establish that 8^(n+1) - 1 is divisible by 7.
8^(n+1) - 1 = 8*8^n - 1 = 7 * (8^n - 1) + (8^n - 1)
Now 7 * (8^n - 1) is divisible by 7 and (8^n - 1) is divisible by 7 by the induction hypothesis so their sum is also divisible by 7.

This proof is much simpler if you ask me since you do not have to worry about the formal definition of 'divisibility' and hence not have to worry about the integer m.

Crbneum

Great work on divisibility and induction. Keep it up woo hoo

mathsgotserved

Waoooo 👌👌👌sir I'm so impressed your way of teaching👍👍👍 I'm from Pakistan

enayahkhan

Thank you so much
Your explanation was very clear and helpful to me!!

oyohval

I had a little trouble understanding that 7(8m+1), but finally got it, xd. Basically, we want to prove that the formula is multiple of 7. So If all equation 8m+1 is multiplying by 7 it mandatory means that its multiple:3 We don't want to prove that the formula has all multiples of 7 though, that's why I wasn't getting it, at the start.

YvtqKn

thanks very much for the videos/lectures . with this, you motivate the spirit of mathematics in up growing mathematicians

enowjordan

Thank you so much it saved me in my exam

PeachIsLive

I have a question which is
(3+√5) ^n + (3- √5)^n

michaelcoker

I'm from Brazil!! thanks you was help me much!!

grazielauzumaki

Can you solve
where n is any positive odd integer
Plz do it

RameshSharma-zgwx

please do a video of the question👉3^2n+1 + 2^2n+1 is divisible by 7

priyankachakraborty

6:25 why is it equals to 7m? pls reply pls

Wendychin

if the bases are the same .then why dont subtract the '1' from both bases?

kdtode

Well of course 7 | 8^n - 1 because k | (k + 1)^n - 1 for natural numbers k and n.

georgemissailidis

make a vedio on 7^n-3^n is divisible by 4

abduljabbar-mbpk

This is a question from my leaving cert maths paper

gracekim

Waoooo 👌👌👌sir I'm so impressed your way of teaching👍👍👍 I'm from Pakistan

enayahkhan

#17 proof prove induction 8^n-1 is divisible by 7 divides mathgotserved induccion

#17 proof prove induction 8^n-1 is divisible by 7 divides mathgotserved induccion

Prove that 8^n-1 is divisible by 7 for all positive integers. Mathematical Induction

Prove 18^n -1 is a multiple of 17. Principle of Mathematical Induction

Induction Divisibility

Induction Divisibility Proof

Proving Divisibility Statement using Mathematical Induction (1)

Proving Divisibility Statements using Mathematical Induction

UPSC VS IIT JEE 🥵 #iitstatus #motivation #toppers #iitjee #jeemains #upscstatus #neet #nit #jee

#16 proof prove induction 3^n less than n+1! inequality induccion matematicas mathgotserved

How to #12 Proof by induction 1^3+2^3+3^3+...+n^3= (n(n+1)/2)^2 n^2(n+1)^2/4 prove mathgotserved

How REAL Men Integrate Functions

Proof that n^3 - n is divisible by 3 using Mathematical Induction

Mathematical Induction - Divisibility Tests (1) | ExamSolutions

NEWYES Calculator VS Casio calculator

Prove that (3n+1)7^n - 1 is divisible by 9 (Mathematical Induction)

Induction with inequalities

#18 prove induction 10^n 3^n is divisible factor divides 7 for all positive integer mathgotserved

#25 Proof Principle of Mathematical Induction inequality factorial is divisible by 8 mathgotserved i

11 years later ❤️ @shrads

Mathematical Induction Examples

Jayesh bhai ignore physics wallah😨 Jayesh Bhai In class#shorts #physicswallah #jayeshop #ncertwallah...

Using Mathematical Induction to Prove 2^(3n) - 3^n is divisible by 5

Jaldi Wahan Se Hato! IIT Delhi version! #iit #iitjee #iitdelhi

Learn how to use mathematical induction to prove a formula