Topic explanation

Standard explanation

P(n): sum = n(n+1)/2. IH: k(k+1)/2. Add k+1: [k(k+1)+2(k+1)]/2 = (k+1)k+22. That is P(k+1).

Key points

• common denominator
• S_k+1 = S_k + a_k+1
• factor after you add
• derive, do not assume
• LINEAR SUM: P(n): sum = n(n+1)/2. IH: k(k+1)/2. Add k+1: [k(k+1)+2(k+1)]/2 = (k+1)k+22. That is P(k+1).
• LINEAR SUM: P(n): sum = n(n+1)/2.
• WHAT — LINEAR SUM: P(n): sum = n(n+1)/2. IH: k(k+1)/2. Add k+1: [k(k+1)+2(k+1)]/2 = (k+1)k+22. That is P(k+1).
• WHY — Why it matters: This rule is a separate learning unit inside induction on sums. It can be defined, applied, and chec

Labelled diagram