Tính nhanh :
A=1/1x2+1/2x3+1/3x4+.......+1/604x605
Tính nhanh
1/1x2+1/2x3+1/3x4+1/4x5+1/5x6
(Nhân ở mẫu số nhé!)
đặt A=1/1x2+1/2x3+1/3x4+1/4x5+1/5x6
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{5}-\frac{1}{6}\)
\(=1-\frac{1}{6}\)
\(=\frac{5}{6}\)
đây là phân số nhé: làm giúp mi~nhon
1. tính nhanh
1/1x2 + 1/2x3 + 1/3x4 + ....... + 1/99x100
thanks
= 1/1-1/2+1/2-1/3+1/3-...-1/100
= 1 - 1/100
= 99/100
\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
1/1x2+1/2x3+1/3x4+1/24x25
1/1x2+ 1/2x3+1/3x4+1/24x25
\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+....+\dfrac{1}{24\times25}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{24}-\dfrac{1}{25}\)
\(=1-\dfrac{1}{25}\)
\(=\dfrac{24}{25}\)
1. Tính nhanh: 1/1x2 + 1/2x3 + 1/3x4 + …+ 1/1981x1982
=1-1/2+1/2-1/3+...+1/1981-1/1982
=1-1/1982
=1981/1982
Lời giải:
$\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+....+\frac{1}{1981\times 1982}$
$=\frac{2-1}{1\times 2}+\frac{3-2}{2\times 3}+\frac{4-3}{3\times 4}+...+\frac{1982-1981}{1981\times 1982}$
$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{1981}-\frac{1}{1982}$
$=1-\frac{1}{1982}=\frac{1981}{1982}$
=1-1/2+1/2-1/3+...+1/1981-1/1982
=1-1/1982
=1981/1982
tính nhanh (1x2)^-1+(2x3)^-1+(3x4)^-1+...+(2014x2015)^-1
a ) A = 2/9x11 + 2/11x13 + 2/13x15 + 2/15x17 + 2/17x19
b ) B = 1/1x2 + 1/2x3 + 1/3x4 + . . . + 1/98x99 + 1/99x100
Các bạn giải qiúp mình , mình cần gấp , tính nhanh nha
1)Tính nhanh:1/1x2+1/2x3+1/3x4+...+1/2014x2015
vì 1/1*2=1-1/2
1/2*3=1/2-1/3
.....................
1/2014*2015=1/2014-1/2015
=1-1/2+1/2-1/3+1/3-....+1/2014-1/2015
=1-1/2015
=2014/2115
\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+....+\frac{1}{2014x2015}\)
=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{99}-\frac{1}{100}\)
=\(1-\frac{1}{100}\)
=\(\frac{99}{100}\)
Tính nhanh :
A = 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + ........1/98x99 + 1/99x100 .
ta có :\(\frac{1}{1\cdot2}=\frac{1}{1}-\frac{1}{2}\)
\(\frac{1}{2\cdot3}=\frac{1}{2}-\frac{1}{3}\)
\(\frac{1}{3\cdot4}=\frac{1}{3}-\frac{1}{4}\)
......
\(\frac{1}{99\cdot100}=\frac{1}{99}-\frac{1}{100}\)
=> \(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=>A=\frac{1}{1}-\frac{1}{100}=\frac{100}{100}-\frac{1}{100}=\frac{99}{100}\)
tính nhanh 1/1x2+1/2x3+1/3x4+ ...+1/2021x2022
nhanh giúp, mik đang cần gấp
A = \(\dfrac{1}{1\times2}\) + \(\dfrac{1}{2\times3}\) + \(\dfrac{1}{3\times4}\)+...+ \(\dfrac{1}{2021\times2022}\)
A = \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\)+...+ \(\dfrac{1}{2021}\) - \(\dfrac{1}{2022}\)
A = 1 - \(\dfrac{1}{2022}\)
A = \(\dfrac{2021}{2022}\)