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![](https://rs.olm.vn/images/avt/0.png?1311)
S = ( 1 - \(\dfrac{1}{2^2}\))(1-\(\dfrac{1}{3^2}\))(1-\(\dfrac{1}{4^2}\))....(1-\(\dfrac{1}{50^2}\))
S = \(\dfrac{2^2-1}{2^2}\).\(\dfrac{3^2-1}{3^2}\).\(\dfrac{4^2-1}{4^2}\)...\(\dfrac{50^2-1}{50^2}\)
Vì em lớp 6 nên phải làm thêm bước này nữa:
Ta có
n2 - 1 = n2 - n + n - 1 = (n2 - n) + (n - 1) = n(n-1) + (n-1) =(n-1)(n+1)
Áp dụng công thức vừa chứng minh trên vào tổng S ta có:
S = \(\dfrac{\left(2-1\right)\left(2+1\right)}{2^2}\).\(\dfrac{\left(3-1\right)\left(3+1\right)}{3^2}\)....\(\dfrac{\left(50-1\right)\left(50+1\right)}{50^2}\)
S = \(\dfrac{1.3}{2^2}\).\(\dfrac{2.4}{3^2}\)......\(\dfrac{49.51}{50^2}\)
S = \(\dfrac{\left(3.4.5.6....49\right)^2.1.2.50.51}{\left(3.4.5.6...49\right)^2.2.2.50.50}\)
S = \(\dfrac{1}{2}\) . \(\dfrac{51}{50}\)
S = \(\dfrac{51}{100}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Trả lời:
a, 5 . 125 . 625 = 5 . 53 . 54 = 58
b, 84 . 165 . 32 = ( 23 )4 . ( 24 )5 . 25 = 212 . 220 . 25 = 237
c, 274 . 8110 = ( 33 )4 . ( 34 )10 = 312 . 340 = 352
a) 5 . 125 . 625 = 5 . 53 . 54 = 51 + 3 + 4 = 58
b) 84 . 165 . 32 = 212 . 220 . 25 = 212 + 20 + 5 = 237
c) 274 . 8110 = 312 . 340 = 312 + 40 = 352
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài làm
\(\left(2x-1\right)^7=x^7\Leftrightarrow2x-1=x\Leftrightarrow x=1\)
\(\left(2x-1\right)^7=x^7\)
\(2x-1=x\)
2x-x=1
X.(2-1)=1
X.1=1
X=1:1
X=1
Vậy x=1
![](https://rs.olm.vn/images/avt/0.png?1311)
=>3025=(x+1)^2 NHỚ K ĐÓ nha bạn
=>x+1=55 hoặc x+1=-55
=>x=54 hoăc x=-56
![](https://rs.olm.vn/images/avt/0.png?1311)
a,\(\dfrac{3^6.5^7.7^{11}}{3^4.5^7.7^{10}}=\dfrac{3^4.3^2.5^7.7^{10}.7}{3^4.5^7.7^{10}}\) \(=9.7=63\)
b,\(\dfrac{2^{43}+2^4}{2^{39}+1}=\dfrac{2^{39}.2^4+2^4}{2^{39}+1}\) \(=\dfrac{2^4\left(2^{39}+1\right)}{2^{39}+1}=16\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, \(390-\left(x-7\right)=13^2:12\)
\(390-\left(x-7\right)=\) \(\dfrac{169}{12}\)
\(x-7=390-\dfrac{169}{12}\)
\(x-7=\dfrac{4511}{12}\)
\(x=\dfrac{4511}{12}+7\)
\(x=\dfrac{4595}{12}\)
Vậy ...
b, \(\left(x-35.2^2\right):7=3^3-24\)
\(\left(x-35.4\right):7=27-24\)
\(\left(x-140\right):7=3\)
\(\Leftrightarrow\left(x-140\right)=3.7\)
\(\Leftrightarrow x-140=21\)
\(\Leftrightarrow x=161\)
Vậy .....
c) \(x-6:2-\left(4^2.3-24\right):2:6=3\)
\(x-3-\left(16.3-24\right):2:6=3\)
\(x-3-\left(48-24\right):2:6=3\)
\(x-3-24:2:6=3\)
\(x-3-2=3\)
\(x=3+2+3\)
\(x=8\)
Vậy ......
d) \(4x-5=5+5^2+5^3+.....+5^{99}\)
Đặt :
\(A=5+5^2+.........+5^{99}\)
\(\Leftrightarrow5A=5^2+5^3+..........+5^{100}\)
\(\Leftrightarrow5A-A=\left(5^2+5^3+......+5^{100}\right)-\left(5+5^2+....+5^{99}\right)\)
\(\Leftrightarrow4A=5^{100}-5\)
\(\Leftrightarrow A=\dfrac{5^{100}-5}{4}\)
\(\Leftrightarrow4x+5=\dfrac{5^{100}-5}{4}\)
Đến đây thì sao nữa nhỉ ?
e) \(\left(2x-1\right)^4=625\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(2x-1\right)^4=5\\\left(2x-1\right)^4=-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=5\\2x-1=-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)
Vậy ....
\(5^x-2-3^2=24\)
\(5^x-2-9=24\)
\(5^x-2=24+9\)
\(5^x-2=33\)
\(5^x=33+2\)
\(5^x=35\)
mà 35 = 5.7 => không có số x nào thỏa mãn điều kiện
Vậy \(x\in\left\{\varnothing\right\}\)
Mình không chắc chắn là đúng hay sai, nếu sai bạn thông cảm!!!