1/1x2 + 1/2x3 + 1/3x4 + ... + 1/99x100
tinh nhanh
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
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 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 = \(\dfrac{2021}{2022}\)
1/1x2+1/2x3+1/3x4+...+1/2023x2024 ?
TRẢ LỜI NHANH . HELP ME
\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+...+\dfrac{1}{2023\times2024}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2023}-\dfrac{1}{2024}\\ =1-\dfrac{1}{2024}=\dfrac{2023}{2024}\)
1/1*2+1/2*3+...+1/2023*2024=1-1/2+1/2-1/3+...+1/2023-1/2024
=1-1/2024=2023/2024
\(...=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2023}-\dfrac{1}{2024}\)
\(=1-\dfrac{1}{2024}=\dfrac{2023}{2024}\)
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