\(\dfrac{1}{25}+\dfrac{1}{36}+\dfrac{1}{49}+...+\dfrac{1}{1521}=\dfrac{1}{5^2}+\dfrac{1}{6^2}+\dfrac{1}{7^2}+...+\dfrac{1}{39^2}>\dfrac{1}{5.6}+\dfrac{1}{6.7}+...+\dfrac{1}{38.39}+\dfrac{1}{39.40}=\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{38}-\dfrac{1}{39}+\dfrac{1}{39}-\dfrac{1}{40}=\dfrac{1}{5}-\dfrac{1}{40}=\dfrac{7}{40}\)