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a)\(A=\frac{1}{5}+\frac{1}{5^2}+....+\frac{1}{5^2^5}\) <=>\(5A=1+\frac{1}{5}+\frac{1}{5^2}+....+\frac{1}{5^{24}}\)
<=>\(5A-A=(1+\frac{1}{5}+...+\frac{1}{5^{24}})-(\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{25}})\)
<=>\(4A=1-\frac{1}{5^{25}}\) <=>\(A=\frac{(5^{25^{ }}-1)}{5^{25}}\div4\)
a: =>x-2/5=3/4:1/3=3/4*3=9/4
=>x=9/4+2/5=45/20+8/20=53/20
b: =>x-2/3=7/3:4/5=7/3*5/4=35/12
=>x=35/12+2/3=43/12
c: 1/3(x-2/5)=4/5
=>x-2/5=4/5*3=12/5
=>x=12/5+2/5=14/5
d: =>2/3x-1/3-1/4x+1/10=7/3
=>5/12x-7/30=7/3
=>5/12x=7/3+7/30=77/30
=>x=77/30:5/12=154/25
e: \(\Leftrightarrow x\cdot\dfrac{3}{7}-\dfrac{2}{7}+\dfrac{1}{2}-\dfrac{5}{4}x+\dfrac{5}{2}=0\)
=>\(x\cdot\dfrac{-23}{28}=\dfrac{2}{7}-3=\dfrac{-19}{7}\)
=>x=19/7:23/28=76/23
f: =>1/2x-3/2+1/3x-4/3+1/4x-5/4=1/5
=>13/12x=1/5+3/2+4/3+5/4=257/60
=>x=257/65
i: =>x^2-2/5x-x^2-2x+11/4=4/3
=>-12/5x=4/3-11/4=-17/12
=>x=17/12:12/5=85/144
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Thiệt hả. Cô cho về nhà nhưng ko bít làm nên cho lên đây mà mình lớp 6 nên ghi bừa vậy thui. xin lỗi những bạn mất chất xắm nhé. Nhưng ai bít làm thì hộ mình nhé.
Câu 13 :
\(\left(-\frac{1}{4}+\frac{5}{8}\right)+-\frac{3}{5}\)
\(=\frac{3}{8}-\frac{-3}{5}\)
\(=\frac{39}{40}\)
Câu 14 :
\(M=\frac{5}{9}.\frac{7}{13}+\frac{5}{9}.\frac{9}{13}-\frac{5}{9}.\frac{3}{13}\)
\(=\frac{5}{9}.\left(\frac{7}{13}+\frac{9}{13}-\frac{3}{13}\right)\)
\(=\frac{5}{9}.1=\frac{5}{9}\)
Câu 15 :
\(E=\left(-\frac{3}{4}+\frac{2}{5}\right):\frac{3}{7}+\left(\frac{3}{5}+\frac{-1}{4}\right):\frac{3}{7}\)
\(E=\left(-\frac{3}{4}+\frac{2}{5}+\frac{3}{5}+\frac{-1}{4}\right):\frac{3}{7}\)
\(E=0\)
Câu 16 :
\(H=\frac{7}{8}:\left(\frac{2}{9}-\frac{1}{8}\right)+\frac{7}{8}:\left(\frac{1}{36}-\frac{5}{12}\right)\)
\(=\frac{7}{8}:\left(\frac{2}{9}-\frac{1}{8}+\frac{1}{36}-\frac{5}{12}\right)\)
\(=\frac{7}{8}:\frac{-7}{24}=-3\)
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`H = 1 - 5 + 5^2 - 5^3 + ... + 5^100`
`5H = 5 - 5^2 + 5^3 - 5^4 + ... + 5^101`
`5H + H = (5 - 5^2 + 5^3 - 5^4 + ... + 5^101) + (1 - 5 + 5^2 - 5^3 + ... + 5^100)`
`6H = 1 + (5 - 5) + (5^2 - 5^2) + ... + (5^100 - 5^100) + 5^101`
`6H = 1 + 5^101`
`H = (1 + 5^101)/6`