At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions.

See more answers at brainly.com

What's the first step? What do I add to both sides? I never know what to add for these questions.

What do I do with that trend?

Yeah, I can. But how did you know to add 2(k+1) to both sides? That's what confuses me.

the integer before k+1 is k

\[2(1)+2(2)+2(3)+...+2(k)+2(k+1)\]

But we know from assuming n=k we had
\[2(1)+2(2)+2(3)+...+2(k)=k^2+k\]

So I replace 2(1)+2(3)+2(3)+...+2(k) with k^2+k
in
2(1)+2(2)+2(3)+...+2(k)+2(k+1)
k^2+k +2(k+1)

Thank you!