Caau6:
\(\dfrac{1}{3^2}+\dfrac{1}{4^2}+\dfrac{1}{5^2}+....+\dfrac{1}{100^2}< \dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-.....-\dfrac{1}{99}+\dfrac{1}{99}-\dfrac{1}{100}\)\(=\dfrac{1}{2}-\dfrac{1}{100}=0,49< 0,5=\dfrac{1}{2}\left(Dpcm\right)\)