Question

[EDG]

\(\frac{1.4}{4.6}+\frac{2.5}{6.8}+\frac{3.6}{8.10}+.........+\frac{48.51}{98.100}\)

Answer 1

[DTD2006ok]

\(\frac{1.4}{4.6}+\frac{2.5}{6.8}+...+\frac{48.51}{98.100}\)

=> \(\frac{1}{4}.\left(\frac{1.4}{2.3}+\frac{2.5}{3.4}+...+\frac{48.52}{49.50}\right)\)

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

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

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

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

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

=> \(\frac{1}{4}.\left[48-2.\frac{12}{25}\right]\)

=> \(\frac{1}{4}.\frac{1176}{25}=\frac{249}{25}\)