Question

a,    \(\frac{1}{5x6}+\frac{1}{6x7}+\frac{1}{7x8}+\frac{1}{8x9}+\frac{1}{9x10}\)

b ,\(\frac{2}{10x12}+\frac{2}{12x14}+\frac{2}{14x16}+.........+\frac{2}{998x1000}\)

.c,  \(\frac{4}{1x2}+\frac{4}{2x3}+\frac{4}{3x4}+........+\frac{4}{69x90}\)

Các bạn giúp mình nhé !

Answer 1

a) \(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)

\(=\frac{1}{5}-\frac{1}{10}\)

\(=\frac{1}{10}\)

b) \(\frac{2}{10.12}+\frac{2}{12.14}+\frac{2}{14.16}+...+\frac{2}{998.1000}\)

\(=\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+\frac{1}{14}-\frac{1}{16}+...+\frac{1}{998}-\frac{1}{1000}\)

\(=\frac{1}{10}-\frac{1}{1000}\)

\(=\frac{99}{1000}\)

c) \(\frac{4}{1.2}+\frac{4}{2.3}+\frac{4}{3.4}+...+\frac{4}{69.90}\)

\(=4.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{89.90}\right)\)

\(=4.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{89}-\frac{1}{90}\right)\)

\(=4.\left(1-\frac{1}{90}\right)\)

\(=4.\frac{89}{90}\)

\(=\frac{178}{45}\)

_Chúc bạn học tốt_

Answer 2

a, \(=\frac{1}{10}\)

Answer 3

a) 1/10

b) ............

c)............

Mình giúp rồi t.i.c.k mình :v

Answer 4

a,\(\frac{1}{5x6}+\frac{1}{6x7}+....+\frac{1}{9x10}\)

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{9}-\frac{1}{10}\)

=\(\frac{1}{5}-\frac{1}{10}\)

\(=\frac{1}{10}\)

Answer 5

\(a)\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)

\(=\frac{1}{5}-\frac{1}{10}=\frac{2}{10}-\frac{1}{10}=\frac{1}{10}\)

Answer 6

a,=\(\frac{1}{5}-\frac{1}{10}\)

\(=\frac{1}{10}\)

b,\(=\frac{1}{10}-\frac{1}{1000}\)

\(=\frac{99}{1000}\)

Answer 7

\(\frac{2}{10\cdot12}+.......+\frac{2}{998\cdot1000}=\frac{1}{10}-\frac{1}{12}+.....+\frac{1}{998}-\frac{1}{1000}=\frac{1}{10}-\frac{1}{1000}\)

Answer 8

a,\(\frac{1}{5x6}+\frac{1}{6x7}+\frac{1}{7x8}+\frac{1}{8x9}+\frac{1}{9x10}\)

=1/5 -1/6 +1/6 -1/7 + 1/7-1/8+1/8-1/9 +1/9-1/10

=1/5 -1/10

=1/10

b,2/10 x 12 +2/12x14+2/14x16 +....+2/998x1000

=1/10 -1/12 +1/12 - 1/14 +1/14 - 1/16 +...+1/998 - 1/1000

=1/10-1/1000

=99/1000

c,4/1x2 + 4/2x3 + 4/3x4 +...+4/89x90

=4x(1/1x2 + 1/2x3 + 1/3x4 +...+1/89x90 )

=4x(1-1/2 + 1/2-1/3 +1/3-1/4+..+1/89 -1/90)

=4x(1-89/90)

=4 x 1/90

=2/45

                                               HOK TỐT NHA BN

Answer 9

b,\(\frac{2}{10x12}+\frac{2}{12x14}+...+\frac{2}{998x1000}\)

\(=\frac{2}{10}-\frac{2}{12}+\frac{2}{12}-\frac{2}{14}+...+\frac{2}{998}-\frac{2}{1000}\)

\(=\frac{2}{10}-\frac{2}{1000}\)

\(=\frac{198}{1000}\)

Tự rút gon

Answer 10

a, thì có người làm rồi

b.đề 

=1/10-1/12+1/12-1/14+1/14-1/16+.......+1/998-1/1000

=1/10-1/1000

=99/1000

c.đề sai phải là 1/89x90

Gọi tổng là a:

a=đề

a/4 = 1/1x2+1/2x3+1/3x4+1/4x5+......+1/89x90

a/4=1-1/1+1/2-1/3+1/3-1/4+1/4-1/5+.......+1/89-1/90

a/4=1-1/90

a/4=89/90

a=89/90 x 4

a=89/360

Answer 11

sửa hộ mk nha:

c,=4x(1-1/90)

  =4x89/90

  =178/45

Answer 12

\(a,\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{9.10}\)

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{9}-\frac{1}{10}\)

\(=\frac{1}{5}-\frac{1}{10}\)

\(=\frac{1}{10}\)

\(b,\frac{2}{10.12}+\frac{2}{12.14}+...+\frac{2}{998.1000}\)

\(=2\left(\frac{1}{10}-\frac{1}{12}+...+\frac{1}{98}-\frac{1}{1000}\right)\)

\(=2\left(\frac{1}{10}-\frac{1}{1000}\right)\)

\(=2.\frac{99}{1000}\)

\(=\frac{99}{500}\)

\(c,\frac{4}{1.2}+\frac{4}{2.3}+...+\frac{4}{69.90}\)

\(=4\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{69}-\frac{1}{90}\right)\)

\(=4\left(1-\frac{1}{90}\right)\)

\(=4.\frac{89}{90}=\frac{178}{45}\)