\(\frac{5}{18.21}+\frac{5}{21.24}+\frac{5}{24.27}+...+\frac{5}{123.126}\)

\(=\frac{5}{3}\left(\frac{3}{18.21}+\frac{3}{21.24}+\frac{3}{24.27}+...+\frac{3}{123.126}\right)\)

\(=\frac{5}{3}\left(\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+\frac{1}{24}-\frac{1}{27}+...+\frac{1}{123}-\frac{1}{126}\right)\)

\(=\frac{5}{3}\left(\frac{1}{18}-\frac{1}{126}\right)\)

\(=\frac{5}{3}.\frac{1}{21}\)

\(=\frac{5}{63}\)

Study well ! >_<

\(\frac{5}{63}\)

\(\frac{5}{18\times21}+\frac{5}{21\times24}+\frac{5}{24\times27}+...+\frac{5}{123\times126}\)

\(=5\times\left(\frac{1}{18\times21}+\frac{1}{21\times24}+...+\frac{1}{123\times126}\right)\)(đoạn này mk àm tắt nhé ^v^)

\(=5\times\frac{1}{3}\times\left(\frac{3}{18\times21}+...+\frac{3}{123\times126}\right)\)

\(=5\times\frac{1}{3}\times\left(\frac{1}{18}-\frac{1}{21}+...+\frac{1}{123}-\frac{1}{126}\right)\)

\(=\frac{5}{3}\times\left(\frac{1}{18}-\frac{1}{126}\right)\)

\(=\frac{5}{3}\times\frac{1}{21}=\frac{5}{63}\)

đúng hay sai mk ko biết đâu nhé!

Gọi tổng bằng S

1/9 S=1/15*18+..................+1/87*90

1/9 S=1/15-1/18+1/18-......................-1/90

1/9 S=1/15-1/90

1/9 S=1/18

S=9/18=1/2

Ta có:

\(\frac{3}{18.21}+\frac{3}{21.24}+\frac{3}{24.27}+...+\frac{3}{123.126}\)

\(=\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+\frac{1}{24}-\frac{1}{27}+...+\frac{1}{123}-\frac{1}{126}\)

\(=\frac{1}{18}-\frac{1}{126}=\frac{1}{21}\)

1/21 nha pn

bạn sai ở đoạn cuối

A=\(\frac{3\cdot3}{15\cdot18}+\frac{3\cdot3}{18\cdot21}+...+\frac{3\cdot3}{96\cdot99}=3\cdot\left(\frac{3}{15\cdot18}+\frac{3}{18\cdot21}+...+\frac{3}{96\cdot99}\right)=3\cdot\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{96}-\frac{1}{99}\right)=3\cdot\left(\frac{1}{15}-\frac{1}{99}\right)=3\cdot\frac{28}{495}=\frac{28}{165}\)

 B8 = 6/15.18 + 6/18.21 + 6/21.24 + ... + 6/87.90

 B8 = 2.(3/15.18 + 3/18.21 + 3/21.24 + ... + 3/87 .90)

 B8 = 2.(1/15 - 1/18 + 1/18 -1/21 + 1/21 - 1/24 + ... + 1/87 - 1/90)

 B8 = 2.(1/15 - 1/90)

 B8 = 2.(6/90 - 1/90)

 B8 = 2. 1/18

 B8 = 1/9

 B = 1/9 : 8

 B = 1/72

thank bạn nha

Ta có :

\(\frac{3}{18x21}+\frac{3}{21x24}+...+\frac{3}{123x126}\)

\(=\frac{3}{18}-\frac{3}{21}+\frac{3}{21}-\frac{3}{24}+...+\frac{3}{123}-\frac{3}{126}\)

\(=\frac{3}{18}-\frac{3}{126}\)

\(=\frac{1}{7}\)

~ Thiên Mã ~

3/(18x21) +3/(21x24) + 3/(24 x 27) + .... +3/(123x 126)

=1/18-1/21+1/21-1/24+...+1/123-1/126

=1/18-1/126

=7/126-1/126

=6/126=1/21

Ohhhh ! Sr bn nhoa =(( Mk lm sai r 

Bn Tôi_Mệt_ Rồi lm ms đúng nhoa

~ Thiên  Mã ~

A = \(\dfrac{4}{3\times6}\) + \(\dfrac{4}{6\times9}\) + ......+ \(\dfrac{4}{18\times21}\)

A = \(\dfrac{4}{3}\) \(\times\) ( \(\dfrac{3}{3\times6}\) + \(\dfrac{3}{6\times9}\)+......+ \(\dfrac{3}{18\times21}\))

A = \(\dfrac{4}{3}\) \(\times\) ( \(\dfrac{1}{3}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{9}\)+.....\(\dfrac{1}{18}\) - \(\dfrac{1}{21}\))

A = \(\dfrac{4}{3}\) \(\times\) ( \(\dfrac{1}{3}\) - \(\dfrac{1}{21}\))

A = \(\dfrac{4}{3}\)\(\times\) \(\dfrac{2}{7}\)

A = \(\dfrac{8}{21}\) 

D=6/15.18+6/18.21+...+6/89.92

D=6(1/15.18+1/18.21+...+1/89.92)

a) 3D=6(1/15-1/18+1/18-1/21+...+1/89-1/92)

3D=6(1/15-1/92)

3D=6.(77/1380)

3D=77/230

D=77/690

b) F=1/25.27+1/27.29+...+1/73.75

2F=2/25.27+2/27.29+..+2/73.75

2F=1/25-1/27+1/27-1/29+...+1/73-1/75

2F=1/25-1/75

2F=2/75

F=1/75

a) đặt  \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}+\frac{1}{256}\)

\(\Rightarrow2\times A=1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{128}\)

\(\Rightarrow2\times A-A=1-\frac{1}{256}\)

\(A=\frac{255}{256}\)

phần b bn cx lm tương tự như z nha!

c) sửa đề:

\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{13x14}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{13}-\frac{1}{14}\)

\(=1-\frac{1}{14}=\frac{13}{14}\)

Sửa:

d) \(\frac{1}{15x18}+\frac{1}{18x21}+\frac{1}{21x24}+...+\frac{1}{87x90}\)

\(=\frac{1}{3}x\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+...+\frac{1}{87}-\frac{1}{90}\right)\)

\(=\frac{1}{3}x\left(\frac{1}{15}-\frac{1}{90}\right)\)

\(=\frac{1}{3}x\frac{1}{18}\)

\(=\frac{1}{54}\)