Create a proof similiar to this one using mathematical induction. PLEASE design as a 2 column proof like the one in the picture.

+ n(n+1) = n(nuo any 3 For each positive integer 1-2+2 3+ Let Sn) = 1.2+2 3+...+ n(n+1) SA? 1(1+1)(1+2) 3 Basis step 1-2 2 1(2)(3) 3 L 2 PE U Inductive Step 1. S(n)=|-2+2+3+-+ (n+1) def of Sh) 2. S(n+1) = 12+2-3+-+ n(n+1)(n+1Yw=2) def of senti) 3. 5() = n(h)(n+2) inductive hypothesis 4. Sid=56) + (n (642) 5.5(41)= (naD(+2) 6+ Din+2) 6. 40+ 1) = (na 13m2) +) factor out (n+1)(n+2) 7.564)= (n+1*+2)/",) lemmon devominator +1) = 2) by 7. by 122. by 3.24. 3 3 this we we prove the claim holds for nt1