Question

Tính Q:

Q= 1.4/4.6 + 2.5/6.8 + 3.6/8.10 + ..... + 48.51/98.100

Answer 1

\(Q=\frac{1}{4}\left(\frac{1.4}{2.3}+\frac{2.5}{3.4}+\frac{3.6}{4.5}+...+\frac{48.51}{49.50}\right)\)

\(=\frac{1}{4}\left(\frac{2.3-2}{2.3}+\frac{3.4-2}{3.4}+\frac{4.5-2}{4.5}+...+\frac{49.50-2}{49.50}\right)\)

\(=\frac{1}{4}\left(1-\frac{2}{2.3}+1-\frac{2}{3.4}+1-\frac{2}{4.5}+...+1-\frac{2}{49.50}\right)\)

\(=\frac{1}{4}\left[48-2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\right)\right]\)

\(=\frac{1}{4}\left[48-2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\right)\right]\)

\(=\frac{1}{4}\left[48-2\left(\frac{1}{2}-\frac{1}{50}\right)\right]=\frac{294}{25}\)