Well, I've got a math problem and for me it's so difficult, so if u don't mind to help it would be amazing <3, its about the mathematical induction method and the ecuation is this:
Use the mathematical induction method to demonstrate the validity of the following equality for all $≥1$
$3+11+⋯+(8−5)=4^2−$
We want to prove that: $$ \sum_{k=1}^{n} (8k-5) = 4n^2 -n $$ First of all, note that the equation is satisfied for $n=1$. Now, assume that the equation holds for $n$. $$ \sum_{k=1}^{n+1} (8k-5) = \sum_{k=1}^{n} (8k-5) + (8(n+1)-5) = (4n^2 -n) + (8n + 3) =4n^2 + 7n +3 = 4(n+1)^2 - (n+1)$$ This concludes the proof by induction.