Question

Tính nhanh:

1/1+2  +  1/ 1+2+3   +    1/1+2+3+4   + .....+    1/1+2+3+4+....+50 = ?

Answer 1

\(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+4+...+50}\)

\(=\frac{1}{\left(1+2\right).2:2}+\frac{1}{\left(1+3\right).3:2}+\frac{1}{\left(1+4\right).4:2}+...+\frac{1}{\left(1+50\right).50:2}\)

\(=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{50.51}\)

\(=2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{50.51}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{50}-\frac{1}{51}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{51}\right)\)

\(=2.\frac{49}{102}=\frac{49}{51}\)

Ủng hộ mk nha ^_-