Question

tính:\(M=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{2}{2004.2005}\)

Answer 1

\(M=\frac{1}{2}+\frac{1}{6}+\frac{1}{10}+....+\frac{2}{2004.2005}\)

\(\Leftrightarrow2M=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+.....+\frac{2}{2004.2005}\)

\(=2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{2004.2005}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{2004}-\frac{1}{2005}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{2005}\right)\)

\(=2.\left(\frac{2005}{4010}-\frac{2}{4010}\right)\)

\(=2.\frac{2003}{4010}\)

\(=\frac{2003}{2005}\)

Answer 2

\(M=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{2}{2004\cdot2005}\)

\(M=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+...+\frac{2}{2004\cdot2005}\)

\(M=2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{2004\cdot2005}\right)\)

\(M=2\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{2004\cdot2005}\right)\)

\(M=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2004}-\frac{1}{2005}\right)\)

\(M=2\left(\frac{1}{2}-\frac{1}{2005}\right)\)

\(M=2\cdot\frac{2003}{4010}\)

\(M=\frac{2003}{2005}\)

Answer 3

dễ mà:

Chú ý vào số cuối cùng nhé bạn nó là dấu hiệu để làm đó

M=2/6+2/12+2/20+.....+2/2004x2005

M=2(1/2x3+1/3x4+.....+1/2004x2005)

M=2(1/2-1/3+1/3-1/4+.....+1/2004-1/2005)

M=2(1-1/2005)

M=2(2004/2005)

M=4008/2005