5

Part of 1993 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

sum 1/n_k =3/17

Source: III - Rioplatense 1993 L3 P5

Prove that for every integer

k \ge 2

k

different natural numbers

n_1

n_2

...

n_k

\frac{1}{n_1}+\frac{1}{n_2}+...+\frac{1}{n_k}=\frac{3}{17}