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\(A=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{54}\right).2.3.4.5...54\)
\(\Rightarrow A=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{54}\right).2.3.4.5...11.12...54\)
\(\Rightarrow\hept{\begin{cases}A⋮5\\A⋮11\end{cases}}\)mà \(\left(5,11\right)=1\) nên \(A⋮55\left(đpcm\right)\)
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a, 1 + 2 + 3 + ... + 87
= (1 + 87).87 : 2
= 87.88 : 2
= 87.44
= 3828
b, 2 + 4 + 6 + ... + 54
= (2 + 54).27 : 2
= 27.56 : 2
= 27.28
= 756
c, 3 + 6 + 9 + ... + 99
= (99 + 3).49 : 2
= 49.102 : 2
= 49.51
= 2499
d, 45.25 + 45.75 + 55.25.25 + 55.75
= 45. (25 + 75) + 55(25.25 + 75)
= 45.100 + 55.700
= 4500 + 38500
= 43000
\(d,45x25+45x75+55x25+55x75\)
\(=45x\left(25+75\right)+55x\left(25+75\right)\)
\(=45x100+55x100\)
\(=100x\left(45+55\right)\)
\(=100x100\)
\(=10000\)
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a ) x = 2
b ) x = 7
c ) x = 5
d ) đề sai ......! hoặc x = rỗng .
e ) x = 5
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Ta có: \(\dfrac{x-1}{59}+\dfrac{x-2}{58}+\dfrac{x-3}{57}=\dfrac{x-4}{56}+\dfrac{x-5}{55}+\dfrac{x-6}{54}\)
\(\Leftrightarrow\dfrac{x-60}{59}+\dfrac{x-60}{58}+\dfrac{x-60}{57}-\dfrac{x-60}{56}-\dfrac{x-60}{55}-\dfrac{x-60}{54}=0\)
\(\Leftrightarrow x-60=0\)
hay x=60
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\(A=5^3+5^4+5^5+...+5^{100}\)
\(A=5^3\left(1+5^1+5^2+...+5^{97}\right)\)
\(A=5^3.\dfrac{5^{97+1}-1}{5-1}=\dfrac{5^3}{4}.\left(5^{98}-1\right)\)
\(\left(2x-1\right).5^4=3.5^5\)
\(2x-1=3.\left(5^5:5^4\right)\)
\(2x-1=3.5\)
\(2x-1=15\)
\(2x=15+1\)
\(2x=16\)
\(x=16:2\)
\(x=8\)
Vậy x = 8
\(a)\left(2x-1\right).5^4=3.5^5\)
\(\left(=\right)\left(2x-1\right).625=3.3125\)
\(\left(=\right)\left(2x-1\right).625=9375\)
\(\left(=\right)2x-1=9375:625\)
\(\left(=\right)2x-1=15\)
\(\left(=\right)2x=15+1\)
\(\left(=\right)2x=16\)
\(\left(=\right)x=16:2\)
\(\left(=\right)x=8\)
Vậy \(x=8\)