1)Tính nhanh:1/1x2+1/2x3+1/3x4+...+1/2014x2015
tính nhanh (1x2)^-1+(2x3)^-1+(3x4)^-1+...+(2014x2015)^-1
1/1x2+1/2x3+1/3x4+...+1/2013x2014+1/2014x2015
1/1*2 + 1/2*3 + 1/3*4 + ... + 1/2013*2014 + 1/2014*2015
= 1 -1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2013 - 1/2014 + 1/2014 - 1/2015
=1-1/2015
=2014/2015
=1-1/2+1/2-1/3+...+1/2014-1/2015
=1-1/2015
=2014/2015
Tính tổng 1x2+2x3+3x4+4x5+.....+2014x2015
Gọi biểu thức trên là A, ta có :
A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 2014x2015
A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 2014x2015x3
A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 2014x2015x(2016-2013)
A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 2014x2015x2016 - 2014x2015x2013.
A x 3 = 2014x2015x2016
A = 2014x2015x2016 : 3
A = 2727117120
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 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 = \(\dfrac{2021}{2022}\)
Tính nhanh:
1/1x2 + 1/2x3 + 1/3x4 +................+ 1/99x100.
Đặt A = 1/1x2 + 1/2x3 + 1/3x4 + .... + 1/99x100
=> A = 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .... + 1/99 - 1/100
=> A = 1 - 1/100
=> A = 99/100
A=\(\frac{-99}{100}\)
hok
tốt
nha
Tính nhanh:
1/1x2 + 1/2x3 + 1/3x4 + ......+ 1/99 x100 = ?
tính nhanh 1/1x2+1/2x3+1/3x4+ ...+1/2021x2022
giúp mik, mik đang cần gấp
1/(1×2) + 1/(2×3) + 1/(3×4) + ... + 1/(2021×2022)
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2021 - 1/2022
= 1 - 1/2022
= 2021/2022
Tính nhanh:
1/1x2+1/2x3+1/3x4+1/3x5+..............1/8x9