Prove that:
1. \(2\dfrac{5}{9}< \dfrac{5}{3}+\dfrac{8}{3^2}+\dfrac{11}{3^3}+...+\dfrac{302}{3^{100}}< 3\dfrac{1}{2}\)
2. \(3\dfrac{7}{9}< \dfrac{7}{3}+\dfrac{13}{3^2}+\dfrac{19}{3^3}+...+\dfrac{601}{3^{100}}< 5\)
3. \(\dfrac{11}{3}+\dfrac{17}{3^2}+\dfrac{23}{3^3}+...+\dfrac{605}{3^{100}}< 7\)
4. \(\dfrac{4}{3}+\dfrac{13}{3^2}+\dfrac{22}{3^3}+...+\dfrac{904}{3^{101}}< \dfrac{17}{4}\)
5. \(\dfrac{7}{3}+\dfrac{11}{3^2}+\dfrac{15}{3^3}+...+\dfrac{403}{3^{100}}< 4,5\)
Quickly, please. :v