Femtobytes
Problem type

Proof by induction for a sum

What it solves
Find the closed formula for a sum such as 1 + 4 + 9 + ... + n squared, and prove it for every natural number n by mathematical induction, with every expansion in the inductive step written out.
Subject
Real Analysis
Topic
Proof by induction
Also called
mathematical induction, prove by induction, sum formula
Your problem

Find a closed formula for this sum and prove it for every natural number nn by induction.

∑i=1ni2\sum_{i=1}^{n} i^{2}
Invent a new one: