Question

[Oh Sehun EXO]

K=\(\frac{4}{2.4}\)+\(\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)

F=\(\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)

I=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2009.2010}\)

Answer 1

[Thắng Nguyễn]

\(K=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)

\(K=2\left(\frac{1}{2}-\frac{1}{2010}\right)\)

\(K=2\times\frac{502}{1005}\)

\(K=\frac{1004}{1005}\)

\(F=\frac{1}{3.6}+\frac{1}{6.9}+...+\frac{1}{30.33}\)

\(3F=\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+...+\frac{1}{30}-\frac{1}{33}\)

\(3F=\frac{1}{3}-\frac{1}{33}\)

\(F=\frac{10}{33}:3\)

\(F=\frac{10}{99}\)

\(I=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2009}-\frac{1}{2010}\)

\(I=1-\frac{1}{2010}\)

\(I=\frac{2009}{2010}\)