Question

S=\(\frac{1}{3}\) +\(\frac{1}{9}\)+\(\frac{1}{18}\)+\(\frac{1}{30}\) +\(\frac{1}{45}\) +\(\frac{1}{63}\) +....+\(\frac{1}{14850}\)

Tính S rồi so sánh S với \(\frac{3}{5}\)

 

Answer 1

S=\(\frac{1}{3}.\left(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{4950}\right)\)

S=\(\frac{1}{3}.2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{99.100}\right)\)

S=\(\frac{2}{3}.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\)

S=\(\frac{2}{3}.\left(1-\frac{1}{100}\right)=\frac{2}{3}.\frac{99}{100}=\frac{33}{50}\)

Answer 2

\(\frac{33}{50}>\frac{30}{50}=\frac{3}{5}->S>\frac{3}{5}\)