= 1/2.(2/1.2.3+2/2.3.4+.....+2/50.51.52

=1/2.(1/1.2-1/2.3+1/2.3-1/3.4+....+1/50.51-1/51.52

=1/2.(1/1.2-1/51.52)

=1/2.(1/2-1/2652)

=1/2.1325/2652

=1325/5304

A=1/1.2-1/2.3+1/2.3-1/3.4+1/3.4-1/4.5+...+1/50.51-1/51.52

A=1/1.2-1/51.52

phần còn lại tự giải nhé

A= \(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{4.5.6}+....+\dfrac{1}{37.38.39}\)

A=\(\dfrac{1}{1}-\dfrac{1}{39}\)

A=\(\dfrac{38}{39}\)

còn lại tự làm do mình có việc chút

Chưa học

\(\frac{15}{37}\)x \(\left(\frac{38}{41}-\frac{74}{45}\right)-\frac{38}{41}\)x \(\left(\frac{15}{37}+\frac{82}{76}\right)\)

\(=\frac{15}{37}\)x \(\frac{38}{41}-\frac{15}{37}\)x \(\frac{74}{45}-\frac{38}{41}\)x \(\frac{15}{37}-\frac{38}{41}\)x \(\frac{82}{76}\)

\(=\frac{15}{37}\)x  \(\frac{38}{41}-\frac{2}{3}-\frac{38}{41}\)x  \(\frac{15}{37}-1\)

\(=\frac{15}{37}\)x  \(\frac{38}{41}\)\(-\frac{38}{41}\)x   \(\frac{15}{37}\)\(-\frac{2}{3}-1\)

\(=0-\frac{2}{3}-1=\frac{-5}{3}\)

đừng chơi với ngu vip

1)

\(=\frac{1}{3}+\frac{12}{67}+\frac{13}{41}-\frac{79}{67}+\frac{28}{41}\)

\(=\frac{1}{3}+\left(\frac{12}{67}-\frac{79}{67}\right)+\left(\frac{13}{41}+\frac{28}{41}\right)=\frac{1}{3}+\left(-1\right)+1=\frac{1}{3}\)

Sửa đề chút nha

\(\frac{x}{2}=\frac{1}{1.2.3}+....+\frac{1}{98.99.100}\)

Ta có công thức tổng quát  \(\frac{1}{a\left(a+1\right)\left(a+2\right)}=\frac{1}{2}\left(\frac{1}{a\left(a+1\right)}-\frac{1}{\left(a+1\right)\left(a+2\right)}\right)\)

\(\Rightarrow\frac{2}{a\left(a+1\right)\left(a+2\right)}=\frac{1}{a\left(a+1\right)}-\frac{1}{\left(a+1\right)\left(a+2\right)}\)

Áp dụng vào tổng ta có

\(\frac{x}{2}=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+....+\frac{1}{98.99}-\frac{1}{99.100}=\frac{1}{2}-\frac{1}{99.100}=\frac{4949}{9900}\)

\(\Rightarrow x=\frac{4949}{4950}\)

Đặt A=(đã cho).

=>2A=2/1*2*3+2/2*3*4+2/3*4*5+...+2/37*38*39.

=>2A=1/1*2-1/2*3+1/2*3-1/3*4+...+1/37*38-1/38*39.

=>2A=1/1*2=1/38*39.

Đến đây tự bấm máy nha.

tk mk nha.

chắc chắn đúng,nay mk làm bài này.

-chúc ai tk mk học giỏi-

good good good !!!

Có \(\frac{1}{1.2.3}=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}\right)\)

      \(\frac{1}{2.3.4}=\frac{1}{2}\left(\frac{1}{2.3}-\frac{1}{3.4}\right)\)

   ...

      \(\frac{1}{17.18.19}=\frac{1}{2}\left(\frac{1}{17.18}-\frac{1}{18.19}\right)\)

=>\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{17.18.19}\)=\(\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{17.18}-\frac{1}{18.19}\right)\)

                                                                           \(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{18.19}\right)=\frac{1}{2}.\frac{1}{2}-\frac{1}{2}.\frac{1}{18.19}< \frac{1}{4}\)

a ) Co :

 1/1.2 - 1/2.3 = 2/1.2.3 

 1/2.3 - 1/3.4 = 2/2.3.4

 ...

 1/37.38 - 1/38.39 = 2/37.38.39

=> 2M = 2/1.2.3 + 2/2.3.4 + ... + 2/37.38.39

=> 2M = 1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + ... + 1/37.38 - 1/38.39

=> 2M = 1/2 - 1/1482

=> 2M = 370/741

=> M = 185/741

B ) A = 1/3 + 1/3^2 + 1/3^3 + ... + 1/3^8

3A = 1 + 1/3 + 1/3^2 + ... + 1/3^7

3A - A = ( 1 + 1/3 + 1/3^2 + ... + 1/3^7 ) - ( 1/3 + 1/3^2 + 1/3^3 + ... + 1/3^8 )

2A = 1 - 1/3^8

A = ( 1 - 1/3^8 ) / 2

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{8.9.10}\)

\(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+..........+\frac{1}{8.9}-\frac{1}{9.10}\)

\(=\frac{1}{1.2}-\frac{1}{9.10}\)

\(=\frac{1}{2}-\frac{1}{90}\)

\(=\frac{45}{90}-\frac{1}{90}\)

\(=\frac{44}{90}\)

\(=\frac{22}{45}\)

22/45