MathDB

Let

n\geq 2

be an integer. For each natural

m

and each integer sequence

0<k_1<k_2<\cdots <k_m

for which

k_1+\cdots+k_m=n

, Michael wrote down the number

\frac{1}{k_1\cdot k_2\cdots k_m}

on the board. Prove that the sum of the numbers on the board is less than

1

P2