a)

`1/3+3/4+2/3+1/4`

`=1/3+2/3+3/4+1/4`

`=1+1`

`=2`

b)

`3/4+3/5+2/8+4/10`

`=3/4+2/8+3/5+4/10`

`=6/8+2/8+6/10+4/10`

`=1+1`

`=2`

c)

`1/10+2/10+3/10+4/10+5/10+6/10+7/10+8/10+9/10`

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

`=1+1+1+1+5/10`

`=4+5/10`

`=40/10+5/10`

`=45/10=9/2`

a: =1/3+2/3+3/4+1/4

=1+1

=2

b: =3/4+1/4+3/5+2/5

=1+1

=2

c: =(1+2+3+4+5+6+7+8+9)/10

=45/10

=9/2

Ta có: \(A=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)\cdot...\cdot\left(1-\dfrac{1}{9}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot\dfrac{4}{5}\cdot...\cdot\dfrac{8}{9}\)

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

a: =17-70-163+246

=-43-163+246

=246-206

=40

a: \(=\dfrac{17}{7}+\dfrac{2}{9}-\dfrac{10}{7}-\dfrac{5}{3}\cdot9=1+\dfrac{2}{9}-15=-14+\dfrac{2}{9}=-\dfrac{126}{9}+\dfrac{2}{9}=-\dfrac{124}{9}\)

b: \(=\dfrac{-11}{23}\left(\dfrac{6}{7}+\dfrac{8}{7}\right)-\dfrac{1}{23}=\dfrac{-22}{23}-\dfrac{1}{23}=-1\)

c: \(=\left(\dfrac{377}{-231}-\dfrac{123}{89}+\dfrac{34}{791}\right)\cdot\dfrac{4-3-1}{24}=0\)

d: \(=\dfrac{12}{7}\left(19+\dfrac{5}{8}-15-\dfrac{1}{4}\right)=\dfrac{12}{7}\cdot\dfrac{35}{8}=\dfrac{15}{2}\)

a: Số số hạng là:

50-1+1=50(số)

Tổng của dãy là:

\(\dfrac{\left(50+1\right)\cdot50}{2}=1275\)

b: Số số hạng là:

(100-2):2+1=50(số)

Tổng của dãy là:

\(\dfrac{\left(100+2\right)\cdot50}{2}=2550\)

a)A=(50+1).50:2=51.50:2=1275

b)B=(100+2).((100-2):2+1):2=98.50:2=2450

Lời giải chi tiết:

tat ca deu bang 10

1+5+1+=?

1+3+8=?

2+4+9=?

a: Ta có: \(\dfrac{8}{9}-\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{72}\right)\)

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

=0

a) \(\dfrac{-5}{9}-\dfrac{4}{15}+\dfrac{2}{9}-\dfrac{11}{15}\)

\(=\left(\dfrac{-5}{9}+\dfrac{2}{9}\right)-\left(\dfrac{4}{15}+\dfrac{11}{15}\right)\)

\(=\dfrac{-3}{9}-\dfrac{15}{15}\)

\(=-\dfrac{1}{3}-1\)

\(=-\dfrac{4}{3}\)

b) \(\dfrac{-8}{13}-\dfrac{7}{16}+\dfrac{21}{13}-\dfrac{1}{6}\)

\(=\left(\dfrac{-8}{13}+\dfrac{21}{13}\right)-\dfrac{7}{16}-\dfrac{1}{6}\)

\(=\dfrac{13}{13}-\dfrac{29}{48}\)

\(=1-\dfrac{29}{48}\)

\(=\dfrac{19}{48}\)

c) \(\dfrac{-15}{25}-\dfrac{14}{21}+\dfrac{8}{5}-\dfrac{5}{3}\)

\(=\dfrac{-3}{5}-\dfrac{2}{3}+\dfrac{8}{5}-\dfrac{5}{3}\)

\(=\left(\dfrac{-3}{5}+\dfrac{8}{5}\right)-\left(\dfrac{2}{3}+\dfrac{5}{3}\right)\)

\(=\dfrac{5}{5}-\dfrac{7}{3}\)

\(=1-\dfrac{7}{3}\)

\(=-\dfrac{4}{3}\)

a: =-5/9+2/9-11/15-4/15

=-3/9-1

=-12/9=-4/3

b: =-8/13+21/13-7/16-1/6

=1-1/6-7/16

=5/6-7/16

=19/48

c: =-15/25+8/5-2/3-5/3

=-7/3+1

=-4/3

a) \(-\dfrac{5}{9}-\dfrac{4}{15}+\dfrac{2}{9}-\dfrac{11}{15}\)

\(=\left(-\dfrac{5}{9}+\dfrac{2}{9}\right)+\left(-\dfrac{4}{15}-\dfrac{11}{15}\right)\)

\(=-\dfrac{1}{3}-1=-\dfrac{4}{3}\)

b) \(-\dfrac{8}{13}-\dfrac{7}{16}+\dfrac{21}{13}-\dfrac{1}{16}\)(sửa đề)

\(=\left(-\dfrac{8}{13}+\dfrac{21}{13}\right)+\left(-\dfrac{7}{16}-\dfrac{1}{16}\right)\)

\(=1-\dfrac{1}{2}=\dfrac{1}{2}\)

c) \(-\dfrac{15}{25}-\dfrac{14}{21}+\dfrac{8}{5}-\dfrac{5}{3}\)

\(=-\dfrac{3}{5}-\dfrac{2}{3}+\dfrac{8}{5}-\dfrac{5}{3}\)

\(=\left(-\dfrac{3}{5}+\dfrac{8}{5}\right)-\left(\dfrac{2}{3}+\dfrac{5}{3}\right)\)

\(=1-\dfrac{7}{3}=\dfrac{-4}{3}\)

Lời giải chi tiết: