Exercise $10.$ To prove summations formulas using mathematical induction the crux of the induction step

relies on finding a connection between summations. We$$ll review these types of induction proofs later in the

course as well as introduce a new induction technique that lends itself to working with recursively defined

sequences.

For m in N$,$ how does

m$+1$

k$=1$

k$3$ relate to

m$$

k$=1$

k$3?$ Be specific. Hint: Write out each sum in expanded form when

m $=5$ and compare. Then generalize for an arbitrary m in N$.$

$3$