ĐẶT BIỂU THỨC LÀ A

Ta có công thức : \(\frac{a}{b.c}=\frac{a}{c-b}.\left(\frac{1}{b}-\frac{1}{c}\right)\)

Dựa vào công thức, ta có :

\(A=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+......+\frac{1}{2013}-\frac{1}{2014}\right)\)

\(A=2.\left(1-\frac{1}{2014}\right)=2.\frac{2013}{2014}=\frac{2013}{1007}\)

Ai thấy đúng thì ủng hộ nha !!!

\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{2013.2014}=2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2013.2014}\right)\)

\(=2.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{2014}-\frac{1}{2015}\right)\)

\(=2.\left(\frac{1}{1}-\frac{1}{2015}\right)=2.\left(\frac{2015}{2015}-\frac{1}{2015}\right)=2.\frac{2014}{2015}=\frac{4028}{2015}\)

ta có:A=\(\frac{2}{1.2}\)+\(\frac{2}{2.3}\)+\(\frac{2}{3.4}\)+...+\(\frac{2}{2013.2014}\)​

=2.(\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+....+\(\frac{1}{2013.2014}\))

=2.(1-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+.....+\(\frac{1}{2013}\)-\(\frac{1}{2014}\))

=2.(1-\(\frac{1}{2014}\))

=2.\(\frac{2013}{2014}\)

 =\(\frac{2013}{1007}\)

chuẩn chưa chuẩn rồi thì tích đúng cho mình  nhé

1/1x2 + 1/2x3 +1/3x4 + ......+1/98x99+1/99x100

=1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +......+ 1/98 - 1/99 + 1/99 + 1/100

=(1-1/100)+(1/2 - 1/2 ) + ( 1/3 - 1/3 ) + ...... + (1/98 - 1/98 ) + ( 1/99 - 1/99 )

= 100/100 - 1/100 + 0 + 0 +.....+ 0 + 0

=99/100

vậy GTBT = 99/100

bn vào câu hỏi tương tự là có

= 1/1 + 1/100

=1011/100

Tích nha

= \(\frac{1x1x1}{1x2x4}x\frac{2.2.1}{1.1.2.2}=\frac{1}{8}.1=\frac{1}{8}\)

=1X2X3/1X2X3X4X2= 1/8                 =3X2X2X2X5/3X2X2X5X2= 1/1

=1/8X1/1=1/8

Tính giá trị biểu thức:

\(\frac{1\times2\times3}{1\times6\times8}\times\frac{6\times4\times5}{3\times2\times2\times10}\)   

\(=\frac{1}{8}\times1=\frac{1}{8}\)

Ủng hộ nha! :) 

\(3C=\frac{3}{1.2.3.4}+\frac{3}{2.3.4.5}+...+\frac{3}{27.28.29.30}\)

\(3C=\frac{4-1}{1.2.3.4}+\frac{5-2}{2.3.4.5}+...+\frac{30-27}{27.28.29.30}\)

\(3C=\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{27.28.29}+\frac{1}{28.29.30}\)

\(3C=\frac{1}{1.2.3}-\frac{1}{28.29.30}\Rightarrow C=\left(\frac{1}{1.2.3}-\frac{1}{28.29.30}\right):3\)

Suy ra 2A=2/1x2x3+2/2x3x4+2/3x4x5+......+2/38x39x40

        2A=3-1/1x2x3+4-2/2x3x4+5-3/3x4x5+........+40-38/38x39x40

       2A=1/1x2-1/2x3+1/2x3-1/3x4+1/4x5-1/5x6+........+1/38x39-1/39x40

      2A=1/2-1/1560

      2A=780/1560-1/1560

      2A=779/1560

     A=779/1560:2

     A=779/1560x1/2

   A=779/3120

\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+.......+\frac{1}{38.39.40}\)

\(2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+.........+\frac{2}{38.39.40}\)

\(2A=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+....+\frac{40-38}{38.39.40}\)

\(2A=\frac{3}{1.2.3}-\frac{1}{1.2.3}+\frac{4}{2.3.4}-\frac{2}{2.3.4}+\frac{5}{3.4.5}-\frac{3}{3.4.5}+.......+\frac{40}{38.39.40}-\frac{38}{38.39.40}\)

\(2A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+.......+\frac{1}{38.39}-\frac{1}{39.40}\)

\(2A=\frac{1}{1.2}-\frac{1}{39.40}\)

\(2A=\frac{1}{2}-\frac{1}{1560}\)

\(2A=\frac{779}{1560}\)

\(A=\frac{779}{1560}:2\)

\(A=\frac{779}{3120}\)

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{2014.2015.2016}\)

\(=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{2014.2015.2016}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{2014.2015}-\frac{1}{2015.2016}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2015.2016}\right)\) 

\(=\frac{1.2}{99.100}\)

\(=\frac{2}{9900}=\frac{1}{4950}\)

A = 5(1/1.2 + 1/2.3 +......+ 1/99.100)

A = 5( 1 - 1/2 + 1/2 - 1/3 +........+ 1/99 - 1/100)

A = 5( 1 - 1/100)

A = 5 . 99/100

A = 99/20

** k mk nha!

\(\frac{5}{1\times2}+\frac{5}{2\times3}+...+\frac{5}{99\times100}=5\left(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{99\times100}\right)=5\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)=5\left(1-\frac{1}{100}\right)=5\times\frac{99}{100}=\frac{99}{20}=4\frac{19}{20}\)

A=5/1-5/2+5/2-5/3+...+5/99-5/100

A=5-(5/2-5/2+5/3-5/3+...5/99-5/99)-5/100

A=5-0+0+0+...+0-5/100

A=5-5/100

A=49/10=4,9

\(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{9\times10}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\)

( GẠCH BỎ CÁC PHÂN SỐ GIỐNG NHAU)

\(=\frac{1}{2}-\frac{1}{10}\)

\(=\frac{5}{10}-\frac{1}{10}\)

\(=\frac{4}{10}=\frac{2}{5}\)

CHÚC BẠN HỌC TỐT!!!!!!!!

\(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+.....+\frac{1}{9\times10}\)

Đặt \(A=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+.....+\frac{1}{9\times10}\)

Nhận xét:

\(\frac{1}{2\times3}=\frac{1}{2}-\frac{1}{3};\frac{1}{3\times4}=\frac{1}{3}-\frac{1}{4}\)

\(\frac{1}{4\times5}=\frac{1}{4}-\frac{1}{5};......;\frac{1}{9\times10}=\frac{1}{9}-\frac{1}{10}\)

Do đó \(A=\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(A=\frac{1}{2}-\frac{1}{10}\)

\(A=\frac{2}{5}\)