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factor of (x^n -y^n )
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take the given proposition as P(n)
prove it for a small natural number say n=1
assume that P(n) is true for n=k and use
that to prove the result for n=k+1
answer and some steps are given below
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other examples:
proof of n^2 < 2^n for every integer n>=5 -----> (mathematical induction problem)
proof of 1^3 +2^3 + 3^3 +...+ n^3 = [ ( n (n+1) ) /2 ] ^2 -----> (mathematical induction problem)
1.2.3 + 2.3.4 + ... +n(n+1) (n+2) = n(n+1)(n+2)(n+3)/4 --------mathematical induction
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formulae on sequences and series
(trig. formulae)
(integration formulae)
(other math problems without classification) or problem index
(formulae on differentiation)
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tags: induction, discrete math, homework help, tutor