m-1-2-m-2-3-m-3-4-m-99-100-99-m-

Question Number 98453 by rb222 last updated on 14/Jun/20

\frac{m}{1 \times 2} \times \frac{m}{2 \times 3} \times \frac{m}{3 \times 4} \times \dots \times \frac{m}{99 \times 100} = 99

m ?

Commented by mr W last updated on 14/Jun/20

\frac{m^{99} \times 1}{(1 \times 2 \times 3 \times \dots \times 99) \times (1 \times 2 \times 3 \times 4 \times \dots \times 100)} = 99

\frac{m^{99}}{99! \times 100!} = 99

m^{99} = 99 \times 99! \times 100!

\Rightarrow m = \sqrt[99]{99 \times 99! \times 100!} \approx 1553.349

Commented by rb222 last updated on 14/Jun/20

t h a n k s s i r

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