(1/4-1)(1/9-1)(1/16-1)..........(1/400-1)
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DT
0
7 tháng 3 2021
Sửa đề: \(B=\left(\dfrac{1}{4}-1\right)\left(\dfrac{1}{9}-1\right)\left(\dfrac{1}{16}-1\right)\cdot...\cdot\left(\dfrac{1}{400}-1\right)\)
Ta có: \(B=\left(\dfrac{1}{4}-1\right)\left(\dfrac{1}{9}-1\right)\left(\dfrac{1}{16}-1\right)\cdot...\cdot\left(\dfrac{1}{400}-1\right)\)
\(=\dfrac{-3}{4}\cdot\dfrac{-8}{9}\cdot\dfrac{-15}{16}\cdot...\cdot\dfrac{-399}{400}\)
\(=\dfrac{-3\cdot8\cdot15\cdot...\cdot399}{4\cdot9\cdot16\cdot...\cdot400}\)
\(=\dfrac{-3\cdot2\cdot4\cdot3\cdot5\cdot...\cdot19\cdot21}{2^2\cdot3^2\cdot4^2\cdot...\cdot20^2}\)
\(=\dfrac{-2\cdot3\cdot4\cdot...\cdot19}{2\cdot3\cdot4\cdot...\cdot20}\cdot\dfrac{3\cdot4\cdot5\cdot...\cdot21}{2\cdot3\cdot4\cdot20}\)
\(=\dfrac{-1}{20}\cdot\dfrac{21}{2}\)
\(=\dfrac{-21}{40}\)
BT
0
31 tháng 3 2017
\(=\frac{-3}{4}.\frac{-8}{9}.\frac{-15}{16}...\frac{-399}{400}\)
KT
2
8 tháng 5 2021
a) $2020.2020-2022.2018$
$ = 2020^2-(2020+2).(2020-2)$
$ = 2020^2 - (2020^2-2^2)$
$ = 4$
b) \(\left(\dfrac{1}{4}-1\right)\left(\dfrac{1}{9}-1\right)\left(\dfrac{1}{16}-1\right)...\left(\dfrac{1}{400}-1\right)\)
\(=\left(\dfrac{1}{2^2}-1\right)\left(\dfrac{1}{3^2}-1\right)\left(\dfrac{1}{4^2}-1\right)...\left(\dfrac{1}{20^2}-1\right)\)
\(=\dfrac{\left(-1\right)\cdot3\cdot\left(-2\right)\cdot4\cdot\left(-3\right)\cdot5\cdot\cdot\cdot\left(-19\right)\cdot21}{2^2\cdot3^2\cdot4^2\cdot\cdot\cdot20^2}\)
\(=-\dfrac{1}{20}\cdot\dfrac{21}{2}=-\dfrac{21}{40}\)
8 tháng 5 2021
Giải:
a) 2020.2020−2022.2018
=20202−(2020+2).(2020−2)
=20202−(20202−22)
=4
b) (1/4−1)(1/9−1)(1/16−1)...(/1400−1)
=(1/22−1)(1/32−1)(1/42−1)...(1/202-1)
=(−1)⋅3⋅(−2)⋅4⋅(−3)⋅5⋅⋅⋅(−19)⋅21/22⋅32⋅42⋅⋅⋅202
=−1/20⋅21/2
=−21/40
LT
0
2N
1
27 tháng 3 2023
\(=\left(1-\dfrac{1}{2}\right)\left(1+\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1+\dfrac{1}{3}\right)\cdot...\cdot\left(1-\dfrac{1}{20}\right)\left(1+\dfrac{1}{20}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{19}{20}\cdot\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{21}{20}\)
=1/20*21/2
=21/40
=-3/4×(-8/9)×(-15/16)×....×(-399/400)
=-3×8×15×....×399/4×9×16×...×400
=-3×2×4×3×5×.....×21×19/2^2×3^2×4^2×....×20^2
=-2×3×4×...×19/2×3×4×...×20 × 3×4×5×....×21/2×3×4×....×20
=-1/20×21/20
=-21/40