1/5 + 4/10 +9/15 + 16/20 + 25/25 + 36/30 + 49/35 + 64/40 + 81/45
=1/5 + 2/5 + 3/5 +...+ 9/5
=45/5=9
\(\frac{1}{5}+\frac{4}{10}+\frac{9}{15}+\frac{16}{20}+\frac{25}{25}+\frac{36}{30}+\frac{49}{35}+\frac{64}{40}+\frac{81}{45}\)
\(=\frac{1}{5}+\frac{1}{5}+\frac{3}{5}+\frac{4}{5}+\frac{5}{5}+\frac{6}{5}+\frac{7}{5}+\frac{8}{5}+\frac{9}{5}\)
\(=\frac{\left(9+1\right)\cdot9:2}{5}=\frac{45}{5}=9\)