Question

tính nhanh tổng sau: S= 3/2-5/6+7/12-9/20 +11/30-13/42+15/56-17/72

giúp mình nha

Answer 1

S=\(\frac{3}{2}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}\)

=>S=\(\frac{1+2}{1.2}-\frac{2+3}{2.3}+\frac{3+4}{3.4}-\frac{4+5}{4.5}+\frac{5+6}{5.6}-\frac{6+7}{6.7}+\frac{7+8}{7.8}-\frac{8+9}{8.9}\)

=>S=

Answer 2

\(S = \dfrac{3}{2} - \dfrac{5}{6} + \dfrac{7}{12} - \dfrac{9}{20} + \dfrac{11}{30} - \) \( \dfrac{15}{42} + \dfrac{15}{56} - \dfrac{17}{72} \)

\(S = \dfrac{1+2}{1.2} + ..... - \dfrac{8 + 9}{8.9} \)

\(S = 1 - \dfrac{1}{2} +\dfrac{1}{2} - \dfrac{1}{3} + ...... + \dfrac{1}{8} -\dfrac{1}{9} \)

\(S = 1 - \dfrac{1}{9} \)

\(S = \dfrac{8}{9}\)

Vậy \(, S = \dfrac{8}{9}\)