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单词 proof by induction
释义 proof by induction

The method of proving a sequence of statements by showing that if one particular case is true, the next must also be true; but it is true for the first, so it must be true for the rest. Consider for example the statement that the sum of the first N terms of a geometric progression a, ar, ar2, etc. is given by SN = a(rN - 1)/(r - 1). This is clearly true for N = 1. Suppose it is true for N. The N + 1th term is arN. But 0198607679.proof-by-induction.1.jpg This is SN with N + 1 substituted for N, so if the formula for SN is correct for N it is correct for N + 1. But we know it is true for N = 1, so it must be true for all N ≥ 1.

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更新时间:2024/6/3 10:12:51