/sci/ - Science & Math

You definitely don't need to use induction to prove those.

1 + 2 + ... + n = n + ... + 2 + 1
Pair up the terms and you get (n+1) + (n+1) + ... n times, so n(n+1).
Divide by 2.
Or
you can b elike derp 1 +2 + ... + n = (n+1) choose 2 by hockey stick done.

For the other one, I think there's a combinatorail way ubt I can't remember it. You can get to it by summing (k+1)^4 - k^4 and telescoping and stuff.