Divisibility Proof (1 of 2: Sum of 7 consecutive integers)

Показать описание

Рекомендации по теме

Комментарии

We could take consecutive integers as n to n+6, we get the sum as 7n +21 and which is 7(n+3)

abhinavdiddigam

You can also do it with n, n+1, n+2, n+3, n+4, n+5, n+6. You then get 7n+21 which you can factor to 7(n+3), which again is divisible by 7.

sammyfromsydney

Eddie, I know you explained why the implication works in both directions verbally but you didn't write anything down to that effect. In an assessment task, what would you be looking for to demonstrate that a student understands the difference between an implication and an equivalence in such a question?

Alge_

Thanks Eddie Woo. Whoever is watching this no that you are the best.

nicolesclass

Wow I just realized that the sum of n consecutive numbers is divisible by n if n is odd. Sum of n alternate numbers is divisible by n if n is even

parikshitbarua

It's funny, when I play Rummikub with my mother and cousins, I use that method to quickly add the value of a sequence of tiles. I just multiply the middle number by how many tiles in the sequence. When they asked me how I knew it would work, I explained the same way, that (n-2)+(n-1)+n+(n+1)+(n+2) is the same as them all being n.

NWAWskeptic

Sir, greetings from India, , sir which software do you use as whiteboard?

touqeerahmed

Could u please tell me how to proof that: the sum of every n consecutive integers is always divisible by 4

LiliSolaimani

Sir could you take lectures on permutations and combinations...please... I know this chapter consists of only basic addition and multiplication but I don't understand how to start the problem and solve... please sir ...I hope you read this and pay some consern...your follower from india..

BronX

I think that this question is similar to a question from the CEMC Gauss 8 exam

danielkim

Can we use Euclid's division lemma to prove this? Starting from the numbers 7q+r

gauravkaloria

8+9+10+11+12+13+14=77, it is also divisible with 7.

vipinchandrabishnoi

Why in solving equations the majority of mathematicians don’t write ⇔, instead, they might write ⇒?

nawaf_ksa

Divisibility Proof (1 of 2: Sum of 7 consecutive integers)

Induction: Divisibility Proofs (1 of 2)

Induction Divisibility

Divisibility Proof (1 of 2: Sum of 7 consecutive integers)

Mathematical Induction with Divisibility: 3^(2n + 1) + 2^(n + 2) is Divisible by 7

Direct Proofs Involving Divisibility

Mathematical Induction - Divisibility Tests (1) | ExamSolutions

Induction - Divisibility Proof (Proving that 4^(n+1) + 5^(2n-1) is divisible by 21)

Number Theory Divisibility Proof

Induction: Divisibility Proof example 1 (n³ + 3n² + 2n is divisible by 6)

Mathematical Induction - Proving Divisibility by 4 (1 of 2: Test and assumption)

Number Theory | Divisibility Basics

Proof: a³ - a is always divisible by 6 (1 of 2: Two different approaches)

Divisibility

Induction - Divisibility Proof (Showing n^2 - 1 is divisible by 8)

DIVISIBILITY - DISCRETE MATHEMATICS

Proving Divisibility Statement using Mathematical Induction (1)

Mathematical Induction - Divisibility

Proving Divisibility Statements using Mathematical Induction

Mathematical Induction Practice Problems

Divisibility tests for 2, 3, 4, 5, 6, 9, 10 | Factors and multiples | Pre-Algebra | Khan Academy

Induction: Divisibility Proof example 5 (8^n+2(7^n)-1 has a factor of 7)

This trick can make your rubik's cube 2x faster😱🔥#ytshorts#shorts#drcuber

Proof By Induction Divisibility

Binomial theorem: Divisibility shortcut SE2 : Show that 11^(n+2)+12^(2n+1) is divisible by 133