đặt A=1+2+3+4+...+n

số số hạng là:

(n-1):2+1

tổng của A là:

(n+1):2.[(n-1):2+1]

A=1+2+3+...+n 

2A =(1+2+3+...+n)+(1+2+3+..+n)

      =(1+n)+(2+n-1)+.+(n-1+2)+(n+1)

      =(n+1) x n

=> A=(n+1) x n/2

B=2+4+6+8...+2.n

  =2 x (1+2+3+..+n)

    =2 x A

  =2 x (n+1) x n/2

 =(n+1) x n

C=1+3+5+7..+(2n+1)

2C=(1+3+5+7..+(2n+1))+(1+3+5+7..+(2n+1))

= (1+2n+1)+(3+2n-1)+...+(2n-1+3)+(2n+1+1)

=(2n+2) x n 

=2 x (n+1) x n

C= (n+1) x n

\(1+2+3+...+n\)

Số số hạng là 

\(\left(n-1\right):1+1=n\)

Tổng đó là

\(\left(n+1\right).n:2=\left(n^2+n\right):2=\frac{n^2+n}{2}\)

Vậy ...

b,c cg làm tương tự nhé

\(\frac{2}{3}\times\frac{1}{5}+\frac{3}{10}\times\frac{2}{3}+\frac{4}{6}\times\frac{1}{2}\)

\(=\frac{2}{3}\times\frac{1}{5}+\frac{3}{10}\times\frac{2}{3}+\frac{2}{3}\times\frac{1}{2}\)

\(=\frac{2}{3}\times\left(\frac{1}{5}+\frac{3}{10}+\frac{1}{2}\right)\)

\(=\frac{2}{3}\times\frac{10}{10}\)

\(=\frac{2}{3}\)

2/3×3/4×4/5÷1/5=2

2/5×3/4×5/6÷3/4=0.33333333333......

2/3 x 3/4 x 4/5 : 1/5 = 6/12 x 4/5 :1/5 = 24/60 :1/5 = 4/10 : 1/5 = 4/10 x 5/1 = 20/10 = 2

2/5 x 3/4 x 5/6 : 3/4 = 6/20 x 5/6 : 3/4 = 3/10 x 5/6  : 3/4 = 15/60 : 3/4 = 1/4 : 3/4 = 1/4 x 4/3 = 4/12 = 1/3

k cho mk nha!

\(\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\div\frac{1}{5}\)

\(=\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{1}\)

\(=\frac{2\times3\times4\times5}{3\times4\times5\times1}\)

\(=\frac{2}{1}\)

\(=2\)

2/3 +5/9 - 3/4 =17/36

2/7 :2/3 -1/7 = 2/7

2/5 * 1/4 :3/8 = 4/15 nha bạn

=17/36

=1/2

=4/15

nhớ tk cho mình nhé

2/3+5/9-3/4=6/9+5/9-3/4=11/8-3/4=11/8-6/8=5/8                                                                                                                                                                                                                                                                                                                                            2/7:2/3-1/7=2/7x3/2-1/7=6/14-1/7=6/14-2/14=4/14                                                                                                                                                                                                                                                                                                                                        2/5x1/4:3/8=2/20x8/3=16/60=4/15

17/16

2/7

4/15

mk nha

2/3 + 5/9 - 3/4

= 11/9 - 3/4

= 17/36

2/7 : 2/3 - 1/7

= 2/7 x 3/2 - 1/7

= 3/7 - 1/7

= 1/2

2/5 x 1/4 : 3/8

= 1/10 : 3/8

= 1/10 x 8/3

= 4/15

3 x \(\frac{4}{11}\) = \(\frac{3}{1}\) x \(\frac{4}{11}\) = \(\frac{12}{11}\)

1 : \(\frac{5}{4}\) = \(\frac{1\times4}{5}\) = \(\frac{4}{5}\)

\(\frac{4}{5}\) x \(\frac{6}{7}\) + \(\frac{2}{3}\) = \(\frac{24}{35}\) + \(\frac{2}{3}\) = \(\frac{142}{105}\)

\(\frac{3}{4}\) + \(\frac{1}{2}\) : \(\frac{5}{6}\) = \(\frac{3}{4}\) + \(\frac{1}{2}\) x \(\frac{6}{5}\) = \(\frac{3}{4}\)+ \(\frac{6}{10}\) \(\frac{27}{20}\)

\(\frac{3}{4}\)+ \(\frac{1}{2}\) = \(\frac{3}{4}\) + \(\frac{2}{4}\)= \(\frac{5}{4}\)

5/7 : 2/3 = 5/7 x 3/2 = 15/14

9/11 : 8 /13 = 9/11 x 13/8 = 117/88

1/8 : 1/6 = 1/8 x 6 = 3/4

4/15 : 7/30 = 4/15 x 30/7 = 8/7

\(\frac{5}{7}:\frac{2}{3}=1\frac{1}{14}\)                  \(\frac{9}{11}:\frac{8}{13}=1\frac{29}{88}\)

\(\frac{1}{8}:\frac{1}{6}=\frac{3}{4}\)                    \(\frac{4}{15}:\frac{7}{30}=1\frac{1}{7}\)\(k\)\(nha\)\(!!!!!!!!!!!!!!\)

5/7:2/3=5x3/7x2=15/14

9/11:8/13=9x13/8x11=117/88

1/8:1/6=1x6/8x1=3/4

4/15:7/30=4x30/7x15=8/7

a)2

b)75/37

c)0

d)8/27

e)7/19

f)4

ok

a) \(\frac{2}{9}+\frac{1}{5}+\frac{7}{9}+\frac{4}{5}=\left(\frac{2}{9}+\frac{7}{9}\right)+\left(\frac{1}{5}+\frac{4}{5}\right)= 1+1=2 \)

b) \(\frac{19}{37}+\left(1+\frac{19}{37}\right)=\left(\frac{19}{37}-\frac{19}{37}\right)+1=0+1=1\)

c) \(\frac{9}{8}-\left(\frac{17}{7}-\frac{3}{7}\right)+\frac{7}{8}=\frac{9}{8}+\frac{7}{8}-\left(\frac{17}{7}-\frac{3}{7}\right)=2-2=0\)

d) \(\frac{3}{5}\times\frac{8}{27}\times\frac{5}{3}=\frac{3}{5}\times\frac{5}{3}\times\frac{8}{27}=1\times\frac{8}{27}=\frac{8}{27}\)

e) \(\frac{7}{19}\times\frac{1}{3}+\frac{7}{19}\times\frac{2}{3}=\frac{7}{19}\times\left(\frac{1}{3}+\frac{2}{3}\right)=\frac{7}{19}\times1=\frac{7}{19}\)

f) \(\frac{12}{5}\times4-4\times\frac{7}{5}=4\times\left(\frac{12}{5}-\frac{7}{5}\right)=4\times1=4\)

Answer:

Bài 1: 

\(\left(135-35\right).\left(-37\right)+37.\left(-42-58\right)\)

\(=100.\left(-37\right)+37.\left(-100\right)\)

\(=\left(-3700\right)+\left(-3700\right)\)

\(=-7400\)

\(-65.\left(87-17\right)-87.\left(17-65\right)\)

\(=\left(-65\right).87-\left(-65\right).17-87.17+87.65\)

\(=-\left(-65\right).17-87.17\)

\(=17.\left(65-87\right)\)

\(=-374\)

\([3.\left(-2\right)-\left(-8\right)].\left(-7\right)-\left(-2\right).\left(-5\right)\)

\(=[\left(-6\right)+8].\left(-7\right)-\left(-2\right).\left(-5\right)\)

\(=2.\left(-7\right)-10\)

\(=-24\)

Bài 2:

\(\left(-55\right).\left(-25\right).\left(-8\right)\)

\(=\left(-55\right).[\left(-25\right).\left(-8\right)]\)

\(=\left(-55\right).200\)

\(=-11000\)

\(\left(-1\right).\left(-2\right).\left(-3\right).\left(-4\right).\left(-5\right).10\)

\(=[\left(-1\right).10].[\left(-2\right).\left(-5\right)].[\left(-3\right).\left(-4\right)]\)

\(=\left(-10\right).10.12\)

\(=-1200\)