bài toán này làm = cách đứt ruột đó




thầy mk vừa dạy mk xong

Ta có: \(\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9900}\)

\(=\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{99.100}\)

 \(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

   \(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)

1/6 + 1/12 + 1/20 + ... + 1/9900
=> 1/2x3 + 1/3x4 + 1/4x5 + ....... + 1/99x100 ------------------------------ Chú ý : 1/2x3 là 1 trên 2x3  các phân số khác cũng zậy 
=> 1/2 x 3 + 1/3 x 4 + 1/ 4 x5 ....... 1/99 x 100 ------------------------ Chú ý : 1/2 x 3 là 1/2 mà nhân vs 3 các phân số khác cũng zậy
=> 1/2 - 1/3 + 1/3 -1/4 + 1/4 - 1/5 + ........ + 1/ 99 - 1/100
=> 1/2 - 1/100
=> 49/100
Ủng hộ mk nha bn
 

= 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 +....+1 /99.100

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

= 1/1 - 1/100

= 100/100 - 1/100

= 99/100

1/2+1/6+1/12+1/20+...+1/9900

=1/1.2+1/2.3+1/3.4+...+1/99.100

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

=1-1/100=99/100

1/2+1/6+1/12+...+1/9900

=1/1.2+1/2.3+1/3.4+...+1/99.100

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

=1-1/100=99/100

1/2 + 1/6 + 1/12 + 1/20 + ... + 1/9900

= 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + ... + 1/99.100

= 1 - 1/2 + 1/2 - 1/2 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/99 - 1/100

= 1 - 1/100

= 99/100 

Mk nhanh nhất đó

Đúng 100%

Tk mk mk tk lại

Cảm ơn bạn nhiều

Thank you very much

( ^ _ ^ )

99/100

Buổi chiều hôm nay cô giáo mới dạy cho mình mà nên mình chắc chắn 100%

= 1-1/2.3-1/3.4-....-1/99.100

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

= 1-1/2+1/100

= 51/100

Tk mk nha

\(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+...+\dfrac{1}{99\cdot100}\)

\(A=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{99}-\dfrac{1}{100}\)

\(A=\dfrac{1}{1}-\dfrac{1}{100}\)

\(A=\dfrac{99}{100}\)

\(\cdot\) LÀ DẤU \(\times\)

A = \(\dfrac{1}{2}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\)+ \(\dfrac{1}{30}\)+.....+ \(\dfrac{1}{9900}\)

A = \(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+....+\dfrac{1}{99\times100}\)

A = \(\dfrac{1}{1}-\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\)+......+ \(\dfrac{1}{99}\) - \(\dfrac{1}{100}\)

A = \(\dfrac{1}{1}\) - \(\dfrac{1}{100}\)

A = \(\dfrac{99}{100}\)

49/100

1/2+1/6+1/12+...+1/9900
=1/(1*2)+1/(2*3)+1/(3*4)+...+1/(99*100)
=1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100
=1-1/100

=99/100

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9900}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}\)

\(=\frac{99}{100}\)

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{9900}\)
\(=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{99\times100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)

Minh Triều làm sai thì tui ko thèm nói mà cứ tui làm sai là mồm anh ta như đàn bà        

\(B=\frac{1}{2}+\frac{1}{6}+...+\frac{1}{9900}=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{99\cdot100}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)\(=\left(1-\frac{1}{100}\right)+\left(\frac{1}{2}-\frac{1}{2}\right)+...\left(\frac{1}{99}-\frac{1}{99}\right)=\left(\frac{100}{100}-\frac{1}{100}\right)+0+...+0=\frac{99}{100}\)Vậy B=99/100

MK k chắc nữa

\(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{9900}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{99.100}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{1}{1}-\frac{1}{100}\)

\(=\frac{100}{100}-\frac{1}{100}\)

\(=\frac{100-1}{100}=\frac{99}{100}\)