a) Đặt A= \(\dfrac{1}{3}+\dfrac{1}{6}+...+\dfrac{1}{36}\)

\(\dfrac{1}{2}\)A=\(\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{72}\)

\(\dfrac{1}{2}\)A=\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{8.9}\)

\(\dfrac{1}{2}\)A=\(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{8}-\dfrac{1}{9}\)

\(\dfrac{1}{2}\)A=\(\dfrac{1}{2}-\dfrac{1}{9}\)

\(\dfrac{1}{2}\)A=\(\dfrac{7}{18}\)

A=\(\dfrac{7}{9}\)

ta có

(1/3+1/6+1/36) +(1/10+1/15+1/45)+(1/21+1/28)

=(\(\frac{12+6+1}{36}\)+\(\frac{9+6+2}{90}\)+\(\frac{4+3}{84}\)

19/36+17/90+1/12

=(19/36+1/12)+17/90

=7/12+17/90

=105/180+34/180

=139/180

1/3 +1/6+1/10+1/15+1/21+1/28+1/36+1/45

=1/1x3+1/3x2+1/2x5+1/3x5+1/3x7+1/7x4+1/4x9+1/9x5

=1/1-1/3+1/3-1/2....+1/9-1/5

=1/1

bạn ơ sao mình tính trong máy tính đc 4/5 mà

Tính

Đặt \(Q=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}\)

\(\Rightarrow\frac{1}{2}\times Q=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)

\(=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}\)

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

\(=\frac{1}{2}-\frac{1}{8}=\frac{4}{8}-\frac{1}{8}=\frac{3}{8}\)

\(\Rightarrow Q=\frac{3}{8}:\frac{1}{2}=\frac{3}{8}\times2=\frac{3}{4}\)

Vậy \(Q=\frac{3}{4}.\)

3/4

HT

\(P=\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+\dfrac{1}{45}\)

\(=2\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\right)\)

\(=2\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\right)\)

\(=2\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\)

\(=2\left(\dfrac{1}{2}-\dfrac{1}{10}\right)=2.\dfrac{2}{5}=\dfrac{4}{5}\)

bn cộng hết lại vs nhau là ra kq!

A =          1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) +  \(\dfrac{1}{10}\) + \(\dfrac{1}{15}\) + \(\dfrac{1}{21}\) + \(\dfrac{1}{28}\) + \(\dfrac{1}{36}\)

A = 2\(\times\) ( \(\dfrac{1}{2}\)  +  \(\dfrac{1}{6}\) + \(\dfrac{1}{12}\) +  \(\dfrac{1}{20}\) + \(\dfrac{1}{30}\) + \(\dfrac{1}{42}\) + \(\dfrac{1}{56}\)+ \(\dfrac{1}{72}\))

A =2\(\times\)( \(\dfrac{1}{1\times2}\)+\(\dfrac{1}{2\times3}\)+\(\dfrac{1}{3\times4}\)+\(\dfrac{1}{4\times5}\)+\(\dfrac{1}{5\times6}\)+\(\dfrac{1}{6\times7}\)+\(\dfrac{1}{7\times8}\)+\(\dfrac{1}{8\times9}\))

A = 2 \(\times\) ( \(\dfrac{1}{1}\)- \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\)+\(\dfrac{1}{3}\)-\(\dfrac{1}{4}\)+...+\(\dfrac{1}{8}\)-\(\dfrac{1}{9}\))

 A = 2\(\times\)( 1 - \(\dfrac{1}{9}\))

A = 2 \(\times\) \(\dfrac{8}{9}\)

A = \(\dfrac{16}{9}\)

tính thẳng đường í: 1/3+1/6+1/10+1/15+1/21+1/28

= 1/2+1/6+1/12=3/4

tinh máy tính đúng đó

kham khảo nha

Câu hỏi của Hà Minh Hiếu - Toán lớp 6 - Học toán với OnlineMath

P=2(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)

P=2((1/2*3)+(1/3*4)+(1/4*5)+(1/5*6)+(1/6*7)+(1/7*8)+(1/8*9)+(1/9*10)

P=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)

P=2(1/2-1/10)

P=2*2/5

P=4/5

H NHA.

\(A=\frac{1}{3}+\frac{1}{6}+...+\frac{1}{28}\)

\(A=\frac{2}{6}+\frac{2}{12}+...+\frac{2}{56}\)

\(A=\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{7.8}\)

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

\(A=2\left(\frac{1}{2}-\frac{1}{8}\right)\)

\(A=2\frac{3}{8}=\frac{3}{4}\)

Ủng hộ mk nha !!! ^_^

\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}\)

\(A=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}\)   (Tử số và mẫu số mỗi phân số nhân với 2 thì giá trị ko thay đổi)

\(A=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}\)

\(A:2=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)

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

\(A:2=\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)

\(A=\frac{3}{8}.2=\frac{3}{4}\)

1/2 N=1/2x3 + 1/3x4 +...+1/9x10 

1/2 N=1/2-1/3+1/3-1/4+...+1/9-1/10

1/2 N=1/2-1/10=2/5

N=2/5:1/2=4/5