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ST
4
28 tháng 6 2018
ta có: 315 < 3158; 3157 < 3158
=> 315 x 3157 < 3158 x 3158
=> A < B
NK
1
6 tháng 3 2023
\(A=\left(\dfrac{456}{2}+1\right)+...+\left(\dfrac{2}{456}+1\right)+\left(\dfrac{1}{457}+1\right)+1\)
\(A=458+\dfrac{458}{2}+....+\dfrac{458}{456}+\dfrac{458}{457}-\dfrac{458}{458}\)
\(A=458\left(\dfrac{1}{2}+...+\dfrac{1}{456}+\dfrac{1}{457}+\dfrac{1}{458}\right)\)
Ta xét \(\dfrac{1}{2}+....+\dfrac{1}{456}+\dfrac{1}{457}+\dfrac{1}{458}\)có :
\(\dfrac{1}{2}=\dfrac{1}{2}\)
\(\dfrac{1}{3}+\dfrac{1}{4}>\dfrac{1}{4}+\dfrac{1}{4}=\dfrac{1}{2}\)
\(\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{8}>\dfrac{1}{8}+\dfrac{1}{8}+...+\dfrac{1}{8}=\dfrac{1}{2}\)
\(\dfrac{1}{9}+\dfrac{1}{10}+....+\dfrac{1}{16}>\dfrac{1}{16}+....+\dfrac{1}{16}=\dfrac{1}{2}\)
\(\dfrac{1}{17}+\dfrac{1}{18}+....+\dfrac{1}{32}>\dfrac{1}{32}+.....+\dfrac{1}{32}=\dfrac{1}{2}\)
\(\dfrac{1}{33}+\dfrac{1}{34}+....+\dfrac{1}{64}>\dfrac{1}{64}+....+\dfrac{1}{64}=\dfrac{1}{2}\)
\(\dfrac{1}{65}+\dfrac{1}{66}+.....+\dfrac{1}{128}>\dfrac{1}{128}+....+\dfrac{1}{128}=\dfrac{1}{2}\)
\(\dfrac{1}{129}+\dfrac{1}{130}+.....+\dfrac{1}{256}>\dfrac{1}{256}+....+\dfrac{1}{256}=\dfrac{1}{2}\)
\(\dfrac{1}{257}+\dfrac{1}{258}+....+\dfrac{1}{458}>\dfrac{1}{458}+...+\dfrac{1}{458}=\dfrac{1}{2}\)
Vậy ta thấy được rằng
\(\dfrac{1}{2}+...+\dfrac{1}{456}>\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{202}{458}\)
\(=4+\dfrac{202}{458}=\dfrac{2034}{458}\)
Vậy \(A>458.\dfrac{2034}{458}=2034\)
Hay tức là A > 2016 ( đpcm )
DP
2
MP
23 tháng 3 2022
Ta có:
A = (457/1 + 1) + (456/2 + 1) + ... + (2/456 + 1) + (1/457 + 1) - 457
A = 458 + 458/2 + ... + 458/456 + 458/457 - 457
A = 458 (1 + 1/2 + ...+ 1/456 + 1/457) - 457
Xét 1 + 1/2 + ... + 1/456 + 1/457, ta có
1 = 1
1/2 = 1/2
1/3 + 1/4 > 1/4 + 1/4 = 1/2
1/5 + 1/6 + ... + 1/8 > 1/8 + 1/8 + ... + 1/8 = 1/2
1/9 + 1/10 +...+ 1/16 > 1/16 + 1/16 +...+ 1/16 = 1/2
1/17 + 1/18 + ... + 1/32 > 1/32 + ... + 1/32 = 1/2
1/33+ 1/34 + ... + 1/64 > 1/64 + ...+ 1/64 = 1/2
1/65 + 1/66 + ...+ 1/128 > 1/128 + ... + 1/128 = 1/2
1/129 + 1/130 + ... + 1/256 > 1/256 + ...+ 1/256 = 1/2
1/257 + 1/258 + ... + 1/457 > 1/457 + ... + 1/457 = 201/457 > 0,4
Vậy 1 + 1/2 + ... + 1/456 + 1/457 > 1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 0,4 = 5,4
Vậy A > 458*5,4 - 457 = 2016,2
Vậy A > 2016.
MP
23 tháng 3 2022
Ta có:
A = (456/2 + 1) + ... + (2/456 + 1) + (1/457 + 1) + 1
A = 458 + 458/2 + ... + 458/456 + 458/457 - 458/458
A = 458 (1/2 + ...+ 1/456 + 1/457 + 1/458)
Xét 1/2 + ... + 1/456 + 1/458, ta có
1/2 = 1/2
1/3 + 1/4 > 1/4 + 1/4 = 1/2
1/5 + 1/6 + ... + 1/8 > 1/8 + 1/8 + ... + 1/8 = 1/2
1/9 + 1/10 +...+ 1/16 > 1/16 + 1/16 +...+ 1/16 = 1/2
1/17 + 1/18 + ... + 1/32 > 1/32 + ... + 1/32 = 1/2
1/33+ 1/34 + ... + 1/64 > 1/64 + ...+ 1/64 = 1/2
1/65 + 1/66 + ...+ 1/128 > 1/128 + ... + 1/128 = 1/2
1/129 + 1/130 + ... + 1/256 > 1/256 + ...+ 1/256 = 1/2
1/257 + 1/258 + ... + 1/458 > 1/458 + ... + 1/458 = 202/458
Vậy 1/2 + ... + 1/456 + 1/457 > 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 202/458 = 4 + 202/458 = 2034/458
Vậy A > 458*2034/458 = 2034
Vậy A > 2016.
9 tháng 12 2023
a: \(\left(3965-2378\right)-\left(437-1378\right)-528\)
\(=3965-2378-437+1378-528\)
\(=\left(3965-437-528\right)-\left(2378-1378\right)\)
\(=3000-1000=2000\)
b: \(\left(-457\right)+\left(-123\right)+23+237\)
\(=\left(-457+237\right)+\left(-123+23\right)\)
\(=-220-100=-320\)
c: \(\left(-329\right)-\left(15-101\right)-\left(25-440\right)\)
\(=-329-15+101-25+440\)
\(=\left(440-15-25\right)+\left(-329+101\right)\)
\(=400-228=172\)
ND
0
A
25 tháng 3 2020
c. TH1:/-8/=8
=8+(-2).3
=8-6=2
TH2:/-8/=8
=-8+(-2).3
=-8.(-6)
=-48
d.-887.(113+457)+113(887-457)
=-887.570+113.430
=-505590+48590
=-457000
e.(16+39)+(158-16-39)
=55+103
=158
25 tháng 3 2020
c, \(\left|-8\right|+\left(-2\right).3\) => \(8+\left(-6\right)\) = \(2\)
d, \(-887.\left(113+457\right)+113.\left(887-457\right)\)
=> \(\left(-887\right).113+\left(-887\right).457+113.887-113.\left(457\right)\)
=> \(\left[\left(-887\right).113+113.887\right]+\left[\left(-887\right).457-113.457\right]\)
=> \(\left[113.\left(887-887\right)\right]+\left[457.\cdot\left(-113-887\right)\right]\)
=> \(\left[113.0\right]+\left(457.-1000\right)\)
=> \(0+-457000=-457000\)
e, \(\left(16+39\right)+\left(158-16-39\right)\)
=> \(\left(16+39+158-16-39\right)\)
=> \(\left(16-16\right)+\left(39-39\right)+158\)
=> \(0+0+158=158\)
5 tháng 8 2023
\(735-\left(457+x\right)=124\)
\(457+x=735-124\)
\(457+x=611\)
\(x=611-457\)
\(x=154\)
Vậy \(x=154\)
5 tháng 8 2023
735 - (457+x)=124
(457 + x) = 735 - 124
457 + x = 611
x = 611 - 457
x = 154
NN
28 tháng 12 2022
\(\left[\left(-457\right)+257\right]+\left[\left(-123\right)+123\right]\)
\(=\left(-200\right)+0=-200\)
NK
28 tháng 12 2022
\(\left(-457\right)+\left(-123\right)+123+257\)
\(=\left[\left(-123\right)+123\right]+\left[\left(-457\right)+257\right]\)
\(=0+\left(-200\right)=-200.\)
CH
23 tháng 11 2023
\(\text{-457+(-123)+23+27}\)
\(\text{= -457-123+23+27}\)
\(\text{= (-457+27) - (123-23)}\)
\(\text{= -430 - 100 = -530}\)
=3158-457-3158+25+457
=(3158-3158)+(457-457)+27
=0+0+27
=27
bằng 27 nh bn