A Strange Operation

★ 7/10SubstitutionalgebraTelescoping

Problem

Define the operation

m∗n=mn+1m+n.m * n = \frac{mn + 1}{m + n}.

Evaluate

(⋯((100∗99)∗98)∗⋯∗3)∗2.\Big(\cdots\big((100 * 99) * 98\big) * \cdots * 3\Big) * 2.

Answer

Solution

Difficulty7/10
TopicsSubstitution, algebra, Telescoping

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