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a) 13/12 

b)  7/8

c)  81/4

d) 20/21

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\) \(+?\)

\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\) \(+?\)

\(=>?=\frac{1}{10\cdot11}=\frac{1}{110}\)

Vậy \(?\) là \(\frac{1}{110}\)

= 0,9 nhé

CHÚC BẠN HỌC GIỎI

TK MÌNH NHÉ

ta có: 1/2=1/1x2

          1/6=1/2x3

           1/12=1/3x4

             1/20=1/4x5

             1/30=1/5x6

                1/42=1/6x7

                 1/56=1/7x8

              1/72=1/8x9

               1/90=1/9x10

                1/110=1/10x11

              tiếp theo bn tiếp tục nhé

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110

=1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10+1/10x1

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11

=1-1/11

=10/11

= 1- ( 1/2 +1/6 +1/12+1/20+1/30+1/42+1/56+1/72+1/89)

=1-721/801

= 80/801

Đề hơi

sai !!
SỬa số 1/89 thành 1/90 hình như ms đúng quy luật !!

\(\frac{8}{9}-\frac{1}{72}-\frac{1}{56}-...-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)

\(=\frac{8}{9}-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{56}+\frac{1}{72}\right)\)

\(=\frac{8}{9}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{7.8}+\frac{1}{8.9}\right)\)

\(=\frac{8}{9}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)\)

\(=\frac{8}{9}-\left(1-\frac{1}{9}\right)\)

\(=\frac{8}{9}-\frac{8}{9}=0\)

thank you nhìu

ta có: 

A= 1/6+1/12+1/20+1/30+1/42+1/56

= 1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8

= 1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8

= 1/2-1/8

= 3/8

vậy A= 3/8

TA CÓ: 

= 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9

= 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/9

=1-1/9

=8/9

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\)

=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\)

= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)

= \(1-\frac{1}{9}\)

= \(\frac{8}{9}\)