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TL
2
LC
25 tháng 6 2015
Số số hạng là: (2x+1-1):2+1=2x:2+1=x+1(số hạng)
Ta có: 1+3+5+…+(2x+1)=400
=> (1+2x+1).(x+1):2=400
=> (2+2x).(x+1):2=400
=> 2.(x+1)(x+1):2=400
=> (x+1)2=202
=> x+1=20
=> x=19
Vậy x=19
22 tháng 8 2023
a) \(215+x=400\)
\(\Rightarrow x=400-215\)
\(\Rightarrow x=185\)
b) \(12,5-2x=\dfrac{1}{5}\)
\(\Rightarrow2x=12,5-\dfrac{1}{5}\)
\(\Rightarrow2x=\dfrac{123}{10}\)
\(\Rightarrow x=\dfrac{123}{10}:2\)
\(\Rightarrow x=\dfrac{123}{20}\)
11 tháng 9 2019
Bài 1 : \(\frac{2}{3}< \left[\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{4}{96}\right]:5\times x< \frac{5}{6}\)
=> \(\frac{2}{3}< \left[\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{1}{24}\right]:5\cdot x< \frac{5}{6}\)
=> \(\frac{2}{3}< \left[\frac{1}{6}+\frac{1}{24}+\frac{2}{15}+\frac{3}{40}\right]:5\cdot x< \frac{5}{6}\)
=> \(\frac{2}{3}< \frac{5}{12}:5\cdot x< \frac{5}{6}\)
=> \(\frac{2}{3}< \frac{1}{12}\cdot x< \frac{5}{6}\)
=> \(\frac{2}{3}< \frac{x}{12}< \frac{5}{6}\)
=> \(\frac{8}{12}< \frac{x}{12}< \frac{10}{12}\)
=> x = 9
Bài 2 : \(\frac{\left[\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right]}{x}=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}\)
=> \(\frac{\left[1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}\right]}{x}=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{11\cdot12}\)
=> \(\frac{\left[1-\frac{1}{16}\right]}{x}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{11}-\frac{1}{12}\)
=> \(\frac{15}{\frac{16}{x}}=1-\frac{1}{12}\)
=> \(\frac{15}{\frac{16}{x}}=\frac{11}{12}\)
=> \(\frac{15}{16}:x=\frac{11}{12}\)
=> \(x=\frac{45}{44}\)
Bài 3 : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\times(x+1):2}=\frac{399}{400}\)
=> \(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\times(x+1)}=\frac{399}{400}\)
=> \(2\left[\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\times(x+1)}\right]=\frac{399}{400}\)
=> \(2\left[\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{x\times(x+1)}\right]=\frac{399}{400}\)
=> \(\left[\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}\right]=\frac{399}{800}\)
=> \(\frac{1}{2}-\frac{1}{x+1}=\frac{399}{800}\)
=> \(\frac{1}{x+1}=\frac{1}{800}\)
=> x = 799
11 tháng 9 2019
Bài 2 :
\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right):x=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}\) (*)
Ta có : \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}=\frac{8}{16}+\frac{4}{16}+\frac{2}{16}+\frac{1}{16}=\frac{8+4+2+1}{16}=\frac{15}{16}\) (1)
Lại có : \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{11.12}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\)
\(=1\left(-\frac{1}{2}+\frac{1}{2}\right)+\left(-\frac{1}{3}+\frac{1}{3}\right)+...+\left(-\frac{1}{11}+\frac{1}{11}\right)-\frac{1}{12}\)
\(=1-\frac{1}{12}=\frac{11}{12}\) (2)
Thay (1) và (2) vào biểu thức (*) ta được :
\(\frac{15}{16}:x=\frac{11}{12}\)
\(\Leftrightarrow x=\frac{15}{16}:\frac{11}{12}\)
\(\Leftrightarrow x=\frac{45}{44}\)
Vậy : \(x=\frac{45}{44}\)
N
2
2 tháng 6 2018
Ta có : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.....+\frac{1}{x\left(x+1\right):2}=\frac{399}{400}\)
\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+.....+\frac{2}{x\left(x+1\right)}=\frac{399}{400}\left(\text{Quy đồng nhé !}\right)\)
\(\Leftrightarrow\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+......+\frac{2}{x\left(x+1\right)}=\frac{399}{400}\)
\(\Leftrightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+......+\frac{1}{x\left(x+1\right)}\right)=\frac{399}{400}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{2}+\frac{1}{3}-\frac{1}{3}+.....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{399}{400}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{399}{400}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{399}{800}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{399}{800}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{800}\)
=> x + 1 = 800
<=> x = 799
2 tháng 6 2018
1/3+1/6+1/10+...+1/x(x+1):2=399/400
2.[1/3.2+1/6.2+1/10.2+...+1/x(x+1)]=399/400
2.[1/6+1/12+1/20+...+1/x(x+1)]=399/400
2.[1/2.3+1/3.4+1/4.5+...+1/x(x+1)]=399/400
1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/x+1=399/800
1/2-1/x+1=399/800
1/x+1=1/800
=> x+1=800
=> x=799
10 tháng 6 2016
a, 27 x 39 + 27 x 63 - 2 x 27
= 27 x ( 39 + 63 - 2 )
= 27 x 100
= 2700
b, 128 x 46 + 128 x 32 + 128x 22
= 128 x ( 46 + 32 + 22 )
= 128 x 100
= 12800
c, 12 x 35 + 35 x 182 - 35 x 94
= 35 x ( 12 + 182 - 94 )
= 35 x 100
= 3500
d, 456 : 2 x 18 + 456 : 3 - 102
= 228 x 18 + 152 - 102
= 4104 + 50
= 4154
HT
10 tháng 6 2016
\(\text{a, 27 x 39 + 27 x 63-2 x 27 =27 x (39+63-2) = 27 x 100 =2700}\)
\(\text{b, 128 x 46 +128 x 32 +128 x 22 =128 x (46+32+22)=128 x 100=12800}\)
\(\text{c , 12 x 35 +35 x 182 -35 x 94 =35 x (12+182-94)=35 x 100=3500.}\)
\(\text{d, 456:2 x 18 +456 :3 -102 =4140+152-102=4190}\)
2,
\(45-\left(x+9\right)=6\Rightarrow45-x-9-6\Rightarrow36-x=6\Rightarrow x=30\)
\(x+7-25=13\Rightarrow x-18=13\Rightarrow x=31\)
\(450:\left(x-19\right)=50\Rightarrow x-19=9\Rightarrow x=28\)
\(4\times\left(x+41\right)=400\Rightarrow x+41=100\Rightarrow x=59\)
\(x+73-26=76\Rightarrow x+47=76\Rightarrow x=31\)
18 tháng 5 2016
bài 1
a, 432 x 25 + 46 x 432 - 432
= 432 x ( 25 + 46 - 1)
=432 x 70
=30 240
b, 432 : 6 - 232 : 6 + 102 : 6
=(432 - 232 +102) : 6
=302:6
=50,333333333333..................
bài 2
a, 285 * x + 115 * x = 400
(285 + 115) * x = 400
400 * x = 400
x = 400 : 400
x = 1
b, x - 6 : 2 - (48 - 24 x 2 : 6 - 3) = 0
x - 3 - (48 - 48 : 6 - 3) = 0
x - 3 - ( 48 - 8 - 3) = 0
x - 3 - 37 = 0
x - 3 = 0 + 37
x - 3 =37
x = 37 + 3
x = 40
18 tháng 5 2016
a) 432x25+46x432-432
=10800+19872-432
=30240
ban oi cau b sai đề hay gì đó
1+3+5+...+(x-2)+x=400
=>\(\dfrac{\left(x-1\right):2+1\cdot\left(1+x\right)}{2}\)=400
=>(\(\dfrac{x}{2}\)-\(\dfrac{1}{2}\)+1)\(\cdot\)(1+x)=800
=>(\(\dfrac{x}{2}\)+\(\dfrac{1}{2}\))\(\cdot\)(1+x)=800
=>(x+1):2\(\cdot\)(1+x)=800
=>(x+1)2=800x2=1600=402
=>x=40-1=39
Vậy x=39.