Mathematical induction is one of the first genuinely new ideas a BCA student meets, and most understand it within a week or two. The marks still go missing — not because the idea is misunderstood, but because the write-up leaves out the parts that are graded. Four things fix it.
- State what you are proving, in full, before you start.
Write the statement P(n) explicitly: “P(n): 1 + 2 + … + n = n(n+1)⁄2.” This single line tells the examiner exactly what you believe you are proving — and it is the line most students skip.
- Give the base case a conclusion, not just a calculation.
“For n = 1: LHS = 1, RHS = 1” is a calculation. Adding “so P(1) is true” turns it into a statement — and that statement is what is actually marked.
- Use the assumption. That is the inductive step.
Assume P(k) is true, write that assumption out explicitly, then show P(k+1) follows from it. If your working for P(k+1) never refers back to the P(k) line, you have not proved anything by induction.
- Close with one sentence, not a silent stop.
“Since P(k) true implies P(k+1) true, and P(1) is true, P(n) is true for all n ≥ 1 by induction” is what closes the proof. Leaving it off costs a mark for the same reason skipping the base case’s conclusion does.
Once this four-part shape is automatic, a new induction problem is mostly a matter of finding the algebra to fill it — the easier half of the question. If proofs are where your BCA maths paper is costing you marks, bring one in to Sector 12 and we will rebuild it together, step by step.
