The Most Classic Proof By Induction

Prove 1+2+...+n = n(n+1)/2 using induction is the most classic proof by induction in mathematics. Let's see how it goes in just 40 seconds! #induction #maths #mathematics #math

🔥Subscribe to 1Psi3Colour:

💥Check out these videos:

👉Check out these playlists:
Math Olympiad Problems from Different Countries:
Functional Equations:

[PranitSuman]

We can also prove this by the formula of sum of 'n' numbers given by Carl Friedrich Gauss when he was just 10 years old.
Let the Arithmetic progression be 1, 2, 3, 4, 5, 6, 7, 8,...n
Here, the first term=1=a
Common difference=1=d
Number of terms= n =n
Using Gauss's formula for calculating sum of terms in an arithmetic progression,
Sum of n terms= n/2[2a+(n-1)d]
Substituting values we get,
Sum of n terms=n/2[2(1)+(n-1)(1)]
Sum of n terms=n/2(2+n-1)
Sum of n terms =n/2(n+1)
Sum of n terms =[n(n+1)]/2

[_quixote]

Bro how’d he just add the k+1 to the entire fraction out of nowhere. I thought we were just replaying it the n with it