\(\frac{4}{9}+\frac{8}{9}+\frac{12}{9}+.............+\frac{52}{9}+\frac{56}{9}\)

\(=\frac{4+8+12+................+52+56}{9}\)

\(=\frac{420}{9}\)

\(=\frac{140}{3}\)

\(\frac{4}{9}+\frac{8}{9}+\frac{12}{9}+...+\frac{56}{9}\)

Tổng trên là tổng cách số hạng cách đều, số hạng sau hơn số hạng trước \(\frac{4}{9}\).

Dãy có số số hạng là: \(\left(\frac{56}{9}-\frac{4}{9}\right)\div\frac{4}{9}+1=14\)(số hạng)

GIá trị của tổng trên là: \(\left(\frac{56}{9}+\frac{4}{9}\right)\times14\div2=\frac{140}{3}\)

3/5+4/7+2/5+1/7+2/7

=(3/5+2/5)+(4/7+1/7+2/7)

=1+1=2

4/9+8/9+12/9+16/9+48/9+56/9+44/9+52/9

=(4/9+16/9)+(8/9+12/9)+(48/9+52/9)+(56/9+44/9)

=20/9+20/9+100/9+100/9

=240/9

=80/3

HT

\(a,\frac{3}{5}+\frac{4}{7}+\frac{2}{5}+\frac{1}{7}+\frac{2}{7}=\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{4}{7}+\frac{1}{7}+\frac{2}{7}\right)=1+1=2\)

\(b,\frac{4}{9}+\frac{8}{9}+\frac{12}{9}+\frac{16}{9}+\frac{48}{9}+\frac{56}{9}+\frac{44}{9}+\frac{52}{9}\)

Phần này bạn xem lại đầu bài nhé!

140/3

Đặt \(A=\frac{4}{9}+\frac{8}{9}+\frac{12}{9}+\frac{16}{9}+...+\frac{48}{9}+\frac{52}{9}+\frac{56}{9}\)

\(\Leftrightarrow\)\(A=\frac{4+8+12+16+...+48+52+56}{9}\)

Dãy \(4;8;12;16;...;48;52;56\):

Có số hạng là : 

\(\left(56-4\right):4+1=14\)

Có tổng là :

\(\left(56+4\right).14:2=420\)

Suy ra \(\frac{4+8+12+16+...+56}{9}=\frac{420}{9}=\frac{140}{3}\)

Vậy tổng đó bằng \(\frac{140}{3}\)

a) \(\frac{3}{5}+\frac{4}{7}+\frac{2}{5}+\frac{1}{7}+\frac{2}{7}\)

\(=\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{4}{7}+\frac{1}{7}+\frac{2}{7}\right)\)

\(=\frac{5}{5}+\frac{7}{7}=1+1=2\)

a) \(\frac{3}{5}+\frac{4}{7}+\frac{2}{5}+\frac{1}{7}+\frac{2}{7}\)

\(=\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{4}{7}+\frac{1}{7}+\frac{2}{7}\right)\)

= 1 + 1

= 2

b) \(\frac{4}{9}+\frac{8}{9}+\frac{12}{9}+\frac{16}{9}+...+\frac{48}{9}+\frac{52}{9}+\frac{56}{9}\)

\(=\frac{4+8+12+16+...+48+52+56}{9}\)

Xét 4 + 8 + 12 + 16 + ... + 48 + 52 + 56

Số các số hạng là: 

      (56 - 4) : 4 + 1 = 14 (số)

4 + 8 + 12 + 16 + ... + 48 + 52 + 56 = (56 + 4) x 14 : 2 = 420

\(\frac{4+8+12+16+...+48+52+56}{9}=\frac{420}{9}=\frac{140}{3}\)

4/9+8/9+12/9+16/9+...+48/9+52/9+56/9
=4+8+12+16+...+48+52+56/9
xét 4+8+12+16+...+48+52+56.
số số hạng là: (56-4):4+1= 14 số
4+8+12+16+...+48+52+56= (56+4)*14:2=420
suy ra: 4+8+12+16+...+48+52+56/9= 420/9
                                                    = 140/3

4/9+8/9+12/9+16/9+..+48/9+52/9+56/9

=4+8+12+16+...+48+52+56/9

xét 4+8+12+16+...+48+52+56

số số hạng là:

(56-4):4+1=14 số

4+8+12+16+...+48+52+56

=(56+4)x14:2=420

=>4+8+12+16+..+48+52+56/9

=420/9=140/3

4/9+8/9+12/9+16/9+...+48/9+52/9+56/9

= 4+8+12+16+...+48+52+56/9

Xét 4+8+12+16+...+48+52+56.

Số số hạng là:

(56-4):4+1= 14 số 4+8+12+16+...+48+52+56

= (56+4)*14:2=420

Suy ra: 4+8+12+16+...+48+52+56/9= 420/9

                                                         = 140/3 

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a) \(...=-\dfrac{12}{46}-\dfrac{15}{21}+\dfrac{3}{7}-\dfrac{7}{23}\)

\(=-\dfrac{12}{46}-\dfrac{7}{23}-\dfrac{15}{21}+\dfrac{3}{7}\)

\(=-\dfrac{6}{23}-\dfrac{7}{23}-\dfrac{5}{7}+\dfrac{3}{7}\)

\(=-\dfrac{13}{23}-\dfrac{2}{7}\)

\(=-\dfrac{13.7}{23.7}-\dfrac{2.23}{23.7}\)

\(=-\dfrac{91}{161}-\dfrac{46}{161}=-\dfrac{137}{161}\)

b) \(...=-21+\dfrac{7}{9}-\dfrac{3}{17}+\dfrac{25}{9}\)

\(=-21-\dfrac{3}{17}+\dfrac{7}{9}+\dfrac{25}{9}\)

\(=-21-\dfrac{3}{17}+\dfrac{32}{9}\)

\(=-\dfrac{3213}{153}-\dfrac{27}{153}+\dfrac{544}{153}=-\dfrac{2696}{153}\)