Question

[lê thị lệ quyên]

1+1/1.2+1/2.3+1/3.4+1/4.5+...+1/2006.2007+1/2007.2008

giúp mình với

Answer 1

[✰๖ۣۜTɾυηɠ ๖ۣۜHσàηɠ✰ (༺TEAM༻꧁༺ɦắ☪☠Áლ...]

\(1+\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2016\cdot2017}+\frac{1}{2017\cdot2018}\)

\(=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}+...+\frac{1}{2016}-\frac{1}{2017}+\frac{1}{2017}-\frac{1}{2018}\)

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

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

\(=\frac{1008}{2018}=\)TỰ RÚT GỌN NHA

Answer 2

[_Shadow_]

\(1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2006.2007}+\frac{1}{2007.2008}\)

\(=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2007}-\frac{1}{2008}\)

\(=2-\frac{2007}{2008}\)

\(=\frac{2009}{2008}\)

~Học tốt~