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Bài 1: Tìm X
a, 32.(x+4)-52=5.22
⇒ 32 .(x+4)-25 =20
⇒9 . (x+4) = 20+25=45
⇒ x+4 = 45: 9 = 5
⇒ x = 5-4 = 1
Vậy x = 1
b,5x+x=39-311:39
⇒ 6x = 39 - 32 =39-9=30
⇒ x = 30 : 6 = 5
Vậy x = 5
c(3x -24 ).73 =2.74
⇒ 3x -24 = 2 . 74 : 73
⇒ 3x - 16 = 2 . 7 = 14
⇒ 3x = 14+16=30
Mà 33=27 , 34 = 81
⇒ x = ∅
Bài 2
a, 66.25+5.66+66.14+33.66
= 66 . ( 25+5+14+33 )
= 66 . 77 = 5082
\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\)\(=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\)
\(=\)\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-...-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)
\(=\)\(1-\dfrac{1}{10}\)
\(=\dfrac{9}{10}\)
a: \(S=\dfrac{-1}{2}\cdot\dfrac{-2}{3}\cdot...\cdot\dfrac{-99}{100}=-\dfrac{1}{100}\)
c: \(5S_3=5^6+5^7+...+5^{101}\)
\(\Leftrightarrow4\cdot S_3=5^{101}-5^5\)
hay \(S_3=\dfrac{5^{101}-5^5}{4}\)
d: \(S_4=7\cdot\left(\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+...+\dfrac{1}{69}-\dfrac{1}{70}\right)\)
\(=7\left(\dfrac{1}{10}-\dfrac{1}{70}\right)=7\cdot\dfrac{6}{70}=\dfrac{6}{10}=\dfrac{3}{5}\)
=(5^1+5^2)+.....+(5^99+5^100)
=5^1*(1+5)+....+5^99*(1+5)
=5^1*^+....+5^99*6
=6*(5^1+....+5^10)
=>5^1+....+5^100 CHIA HẾT CHO 6 NK
\(\frac{-5}{6}+\frac{8}{3}+\frac{29}{-6}\le x\le\frac{-1}{2}+2+\frac{5}{2}\)
\(\Rightarrow-3\le x\le4\)
\(\Rightarrow x\in\left\{-3;-2;-1;0;1;2;3;4\right\}\)
\(\left(\frac{-2}{3}-\frac{1}{2}\right):\frac{-1}{4}\le x\le\left(\frac{-5}{6}+\frac{9}{4}:\frac{-3}{2}\right)\cdot\frac{-13}{2}\)
\(\Rightarrow\frac{14}{3}\le x\le\frac{91}{6}\)
\(\Rightarrow\frac{28}{6}\le x\le\frac{91}{6}\)
\(\Rightarrow x\in\left\{\frac{28}{6};\frac{29}{6};...;\frac{90}{6};\frac{91}{6}\right\}\)
a) 13 + 23 + 33 + 43 + 53
= 1 + 8 + 27 + 64 + 125
= 9 + 27 + 64 + 125
= 36 + 64 + 125
= 100 + 125
= 225
<=> 225 = 152
b) 13 + 23 + 33 + 43 + 53 + 63
= 1 + 8 + 27 + 64 + 125 + 216
= 9 + 27 + 64 + 125 + 216
= 36 + 64 + 125 + 216
= 100 + 125 + 216
= 225 + 216
= 441
<=> 441 = 212
B=1/15+1/35+1/63+1/99+1/143
B=1/3.5+1/5.7+1/7.9+1/9.11
B=1/2.(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
B=1/2.(1/3-1/11)
B=1/2.8/33
B=4/33