a.=7-(1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7 + 1/7x8 )
= 7- [ 1 - 1/8 ]
= 7 - 7/8
= 49/8
b.=1997x 1995 + 1997 - 995 / 1997 x 1995 + 1002
=1997-995/1002
=1
còn câu cuối để mình nghĩ
\(E=\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}\)
\(E=\frac{1}{2}+\frac{6-1}{6}+\frac{12-1}{12}+\frac{20-1}{20}+\frac{30-1}{30}+\frac{42-1}{42}+\frac{56-1}{56}\)
\(E=\frac{1}{2}+\frac{6}{6}-\frac{1}{6}+\frac{12}{12}-\frac{1}{12}+\frac{20}{20}-\frac{1}{20}+\frac{30}{30}-\frac{1}{30}+\frac{42}{42}-\frac{1}{42}+\frac{56}{56}-\frac{1}{56}\)
\(E=\frac{1}{1x2}+1+1+1+1+1+1-\left(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}+\frac{1}{6x7}+\frac{1}{7x8}\right)\)
\(E=1-\frac{1}{2}+6-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\right)\)
\(E=1-\frac{1}{2}+6-\left(\frac{1}{2}-\frac{1}{8}\right)\)
\(E=1-\frac{1}{2}+6-\frac{1}{2}+\frac{1}{8}\)
\(E=6+\frac{1}{8}=\frac{49}{8}\)
\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}\)
\(=1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+1-\frac{1}{30}+1-\frac{1}{42}+1-\frac{1}{56}\)
\(=7-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\right)\)
\(=7-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{.1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\right)\)
\(=9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\right)\)
\(=7-\left(1-\frac{1}{8}\right)\)
\(=\frac{49}{8}\)
