Question

\(S=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2017.2018}\)

Answer 1

\(S=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\)

\(\Rightarrow S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2017}-\frac{1}{2018}\)

\(\Rightarrow S=\frac{1}{2}-\frac{1}{2018}\)

\(\Rightarrow S=\frac{1008}{2018}\)

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Answer 2

\(S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{2017}-\frac{1}{2018}\)

\(S=\frac{1}{2}-\frac{1}{2018}\)

\(S=\frac{504}{1009}\)

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Answer 3

S = \(\frac{1}{2.3}\)+ \(\frac{1}{3.4}\) + \(\frac{1}{4.5}\)+ ..... + \(\frac{1}{2017.1018}\)

S = \(\frac{1}{2}\) - \(\frac{1}{3}\)+ \(\frac{1}{3}\)- \(\frac{1}{4}\)+ \(\frac{1}{5}\) + .....+ \(\frac{1}{2017}\)- \(\frac{1}{2018}\)

S = \(\frac{1}{2}\) - \(\frac{1}{2018}\)

S = \(\frac{1008}{2018}\)

CHÚC BẠN HỌC GIỎI

Answer 4

\(S=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2017.2018}\)

\(\Rightarrow S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2017}-\frac{1}{2018}\)

\(\Rightarrow S=\frac{1}{2}-\frac{1}{2018}\)

\(\Rightarrow S=\frac{1009}{2018}-\frac{1}{2018}\)

\(\Rightarrow S=\frac{1008}{2018}\)

\(\Rightarrow S=\frac{504}{1009}\)

Chúc bạn học tốt !!!