Mathematical Induction - Proof of ∑r=n(n+1)/2 | ExamSolutions

Here you are shown how to prove by mathematical induction the sum of the series for r ∑r=n(n+1)/2

[cipherunity]

There is a simple solution of this problem for those who are not aware of mathematical induction.

Let S1 = 1 + 2 + 3 + . . . +(n-2)+(n-1)+(n)

We can also write by re-arranging

S1 = (n) + (n-1) + (n-2)+ . . . + 3 + 2 + 1

Adding both equations

2S1 = (n+1) + (n+1) +( n+1) + . . . +(n+1) + (n+1) + (n+1) n terms

2S1 = n (n+1)

Hence S1 = n (n+1)/2
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[chidochiradza]

my exam is in an hour 30 and i just found this precious video which just saved my life

[davellew]

I`m relly sorry but you have confused me even more

[topaussiemezza]

I watched your induction videos a number of months ago & I gotta say they're basically the best I've ever fucking seen on YouTube. Helped me to like induction & see how easy it actually is. Sarada Herke does good proofs in graph theory, too. Other uploaders I've seen are just overrated & don't even cover different induction scenarios like these videos.

[EddieBlundell]

Thankyou! The last bit helped things click for me, I'm using proof by induction whilst studying recursion. As it's true for the base case, and we've proved it's true for k+1, we know it's true for 2 and so on.

[benzola]

i bet you won't get a better explanation than this....

[fireyonghan]

Thank you. Gotta be flexible and embrace the dots.