Question

Prove using mathematical induction that for all n greater than or equal to 1 + 4 + 7 + ……. + (3n – 2) = n(3n-1)/2  for all n ∈ N.

Answer 1

Let p(n) : 1 + 4 +7 + ..+ (3n - 2) = \(\frac{n(3n-1)}{2}\)

Put n = 1

LHS = 1

RHS = \(\frac{1(3-1)}{2}=1\)

∴ P(1) is true

Assume P(k) is true for n = k.

∴ P(k+1) is true whenever p(k) is true.

∴ By the principle of Mathematical induction, p(n) is true for all n ε N.