Cho biết
\(1^{2+2^2+3^2+.......+10^2=385}\)
Tính tổng:
a)\(^{2^2+4^2+6^2+........+20^2}\)
b)\(\left(0,25\right)^2+\left(0,5\right)^2+...........+\left(2,5\right)^2\)
K
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IM
10 tháng 9 2016
Ta có :
\(S=\left(0,25\right)^2+\left(0,5\right)^2+...+\left(2,5\right)^2\)
\(\Rightarrow4S=2^2.\left(0,25\right)^2+2^2.\left(0,5\right)^2+.....+2^2.\left(2,5\right)^2\)
\(\Rightarrow4S=1^2+2^2+....+10^2\)
\(\Rightarrow4S=385\)
\(\Rightarrow S=\frac{385}{4}\)
T
22 tháng 2 2020
C = \(25.\left(\frac{-1}{3}\right)^3\) \(+\frac{1}{5}\) \(-2.\left(\frac{-1}{2}\right)^2\) \(-\frac{1}{2}\)
C = \(25.\left(\frac{-1}{27}\right)+\frac{1}{5}\) \(-2.\frac{1}{4}\) \(-\frac{1}{2}\)
C = \(\frac{-25}{27}\) \(+\frac{1}{5}\) \(-\frac{1}{2}\) \(-\frac{1}{2}\)
C = \(\frac{-25}{27}\) \(+\frac{1}{5}\) \(-1\)
C = \(\frac{-125}{135}\) \(+\frac{27}{135}\) \(-\frac{135}{135}\)
C = \(\frac{-233}{135}\)
D = \(-8.\left(\frac{3}{4}-\frac{1}{4}\right):\left(\frac{9}{4}-\frac{7}{6}\right)\)
D = \(-8.\frac{1}{2}\) \(.\frac{12}{13}\)
D = \(-4.\frac{12}{13}\)
D = \(\frac{-48}{13}\)
E = \(5\sqrt{16}\) \(-4\sqrt{9}\) \(+\sqrt{25}\) \(-0,3\sqrt{400}\)
E = \(5.4-4.3+5-0,3.20\)
E = \(20-12+5-6\)
E = \(8+\left(-1\right)\)
E = \(7\)
F = \(\left(\frac{-3}{2}\right)\) \(+\left|\frac{-5}{6}\right|\) \(-1\frac{1}{2}\) \(:6\)
F = \(\left(\frac{-3}{2}\right)\) \(+\frac{5}{6}\) \(-\frac{3}{2}\) \(.\frac{1}{6}\)
F = \(\left(\frac{-3}{2}\right)\) \(+\frac{5}{6}\) \(-\frac{1}{4}\)
F = \(\left(\frac{-18}{12}\right)\) \(+\frac{10}{12}\) \(-\frac{3}{12}\)
F = \(\frac{-11}{12}\)
Chúc cậu hk tốt ~
LA
7 tháng 4 2018
\(A=\left(3\dfrac{1}{3}+2,5\right):\left(3\dfrac{1}{6}-4\dfrac{1}{5}\right)-\dfrac{11}{31}\\ =\left(\dfrac{10}{3}+\dfrac{5}{2}\right):\left(\dfrac{19}{6}-\dfrac{21}{5}\right)-\dfrac{31}{11}\\ =\left(\dfrac{30}{6}+\dfrac{15}{6}\right):\left(\dfrac{95}{30}-\dfrac{126}{30}\right)-\dfrac{31}{11}\\ =\dfrac{45}{6}:\dfrac{-21}{30}-\dfrac{31}{11}\\ =\dfrac{15}{2}\times\dfrac{-10}{7}-\dfrac{31}{11}=-\dfrac{75}{7}-\dfrac{31}{11}=-\dfrac{825}{77}-\dfrac{217}{77}=\dfrac{-1042}{77}\)
LA
7 tháng 4 2018
\(B=\left(-6\right).10:\left[-0,25+\dfrac{1}{2}:\left(-2\right)\right]+1\dfrac{3}{4}\\ =-60:\left(\dfrac{-1}{4}+\dfrac{1}{2}.\dfrac{-1}{2}\right)+1\dfrac{3}{4}\\ =-60:\left(\dfrac{-1}{4}+\dfrac{-1}{4}\right)+1\dfrac{3}{4}\\ =-60:\left(\dfrac{-1}{2}\right)+1\dfrac{3}{4}=120+1\dfrac{3}{4}=121\dfrac{3}{4}\)
NT
26 tháng 10 2016
Ta thấy A gấp 12+22+....+102 4 lần nên Tổng A gấp 4 lần nó
=> A=385.4=1540
24 tháng 3 2017
tại sao A lại gấp 12+22+.......+102 4 lần vậy,bạn giải thích rõ đc ko?
2 tháng 10 2021
a: \(\left(0.5\right)^3\cdot2^3=1\)
b: \(\left(0.25\right)^2\cdot16=1\)
c: \(\left(\dfrac{3}{5}\right)^3:\left(-\dfrac{27}{1000}\right)=\dfrac{3^3}{5^3}\cdot\dfrac{-1000}{27}=\dfrac{-1000}{125}=-8\)
20 tháng 1 2020
a) 4x - 3 = 4- 3x
<=> 4x + 3x = 4 + 3
<=> 7x = 7
<=> x = 1
b) 3 + (x - 5) = 2 ( 3x - 2)
<=> 3 + x - 5 = 6x - 4
,<=> x- 2 = 6x - 4
<=> 4 - 2 = 6x - x
<=> 2 = 5x
,<=> 5x = 2
<=> x = \(\frac{2}{5}\)
c) 2( x - \(\frac{1}{4}\)) - 4 = -6 ( -\(\frac{1}{3}\)+ 0,5) + 2
<=> 2x -\(\frac{1}{2}\)- 4 = 2 - 3 + 2
<=> 2x- \(\frac{9}{2}\)= 1
,<=> 2x = 1 + \(\frac{9}{2}\)= \(\frac{11}{2}\)
<=> x = \(\frac{11}{4}\)
d) 2 ( x - 0,5) + 3 = 0,25 ( 4x - 1)
<=> 2x - 1 + 3 = x - 0,25
<=> 2x + 2 = x - 0,25
<=> 2x - x = -2 - 0,25
<=> x = -2
\(a,2^2+4^2+6^2+...+20^2\)
\(=1^2.2^2+2^2.2^2+3^2.2^2+...+10^2.2^2\)
\(=\left(1^2+2^2+3^2+...+10^2\right).2^2\)
\(=385.4\)
\(=1540\)
\(b,\left(0.25\right)^2+\left(0.5\right)^2+...+\left(2.5\right)^2\)
\(=1^2.0,25^2+2^2.0,25^2+...+10^2.0,25^2\)
\(=\left(1^2+2^2+...+10^2\right).0,25^2\)
\(=385.0.0625\)
\(=24.0625\)
a/ Có tự ghi lại đề
= ((2+8)+(4+6)+10+(12+18)+(14+16)+20))^2
= ((10+10+10+30+30+20))^2
=(110)^2
=100^2+10^2
=10000+100
=10100