Discrete Mathematics, Mathematics, Mathematics Education, Study Guide, Computer Science.
4+8+12+⋯+4𝑛𝑛=2𝑛𝑛2+2𝑛𝑛 Proof By mathematical induction: 1. Basis case: 𝑛𝑛=1 The left-hand side (LHS) =4=2(1)2+2(1)=4= The right-hand side (RHS) 2. Assume for some integer 𝑘𝑘≥1, that 4+8+12+⋯+4𝑘𝑘=2𝑘𝑘2+2𝑘𝑘 WTST 4+8+12+⋯+4(𝑘𝑘+1)=2(𝑘𝑘+1)2+2(𝑘𝑘+1) that is 4+8+12+⋯+4(𝑘𝑘+1)=2𝑘𝑘2+6𝑘𝑘+4 LHS