Những câu hỏi liên quan
Tính các biểu thức sau
a,2/1x3x5+2/3x5x7+2/5x7x9+2/7x9x11
b,1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6
Tính nhanh các biểu thức sau:
a,2/1x3x5+2/3x5x7+2/5x7x9+2/7x9x11
b,1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6
A = \(\dfrac{2}{1\times3\times5}\) + \(\dfrac{2}{3\times5\times7}\) + \(\dfrac{2}{5\times7\times9}\)+\(\dfrac{2}{7\times9\times11}\)
A = \(\dfrac{1}{2}\) x (\(\dfrac{4}{1\times3\times5}\) + \(\dfrac{4}{3\times5\times7}\) + \(\dfrac{4}{5\times7\times9}\) + \(\dfrac{4}{7\times9\times11}\))
A = \(\dfrac{1}{2}\)x (\(\dfrac{1}{1\times3}\)-\(\dfrac{1}{3\times5}\)+\(\dfrac{1}{3\times5}\)-\(\dfrac{1}{5\times7}\)+\(\dfrac{1}{5\times7}\)-\(\dfrac{1}{7\times9}\)+\(\dfrac{1}{7\times9}\)-\(\dfrac{1}{9\times11}\))
A = \(\dfrac{1}{2}\)x (\(\dfrac{1}{1\times3}\) - \(\dfrac{1}{9\times11}\))
A = \(\dfrac{1}{2}\) x (\(\dfrac{1}{3}-\dfrac{1}{99}\))
A = \(\dfrac{1}{2}\times\) \(\dfrac{32}{99}\)
A = \(\dfrac{16}{99}\)
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B = \(\dfrac{1}{1\times2\times3}\) + \(\dfrac{1}{2\times3\times4}\) + \(\dfrac{1}{3\times4\times5}\) + \(\dfrac{1}{4\times5\times6}\)
B = \(\dfrac{1}{2}\) x (\(\dfrac{2}{1\times2\times3}+\dfrac{2}{2\times3\times4}+\dfrac{2}{3\times4\times5}+\dfrac{2}{4\times5\times6}\))
B = \(\dfrac{1}{2}\) x (\(\dfrac{1}{1\times2}\)-\(\dfrac{1}{2\times3}\) + \(\dfrac{1}{2\times3}\)-\(\dfrac{1}{3\times4}\)+\(\dfrac{1}{3\times4}\)-\(\dfrac{1}{4\times5}\)+\(\dfrac{1}{4\times5}\)-\(\dfrac{1}{5\times6}\))
B = \(\dfrac{1}{2}\)x(\(\dfrac{1}{1\times2}\) - \(\dfrac{1}{5\times6}\))
B = \(\dfrac{1}{2}\)x (\(\dfrac{1}{2}-\dfrac{1}{30}\))
B = \(\dfrac{1}{2}\)x \(\dfrac{7}{15}\)
B = \(\dfrac{7}{30}\)
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Chứng minh rằng:A=36/1x3x5+36/3x5x7+36/5x7x9+....+36/25x27x29
\(A=9\left(\dfrac{4}{1\cdot3\cdot5}+\dfrac{4}{3\cdot5\cdot7}+...+\dfrac{4}{25\cdot27\cdot29}\right)\)
\(=9\left(\dfrac{1}{1\cdot3}-\dfrac{1}{3\cdot5}+\dfrac{1}{3\cdot5}-\dfrac{1}{5\cdot7}+...+\dfrac{1}{25\cdot27}-\dfrac{1}{27\cdot29}\right)\)
\(=9\left(\dfrac{1}{3}-\dfrac{1}{783}\right)=\dfrac{260}{87}\)
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A=1/1x2x3+1/2x3x4+1/3x4x5+...+1/18x19x20<1/4
Ta có:
\(A=\frac{1}{1\text{x}2\text{x}3}+\frac{1}{2\text{x}3\text{x}4}+\frac{1}{3\text{x}4\text{x}5}+...+\frac{1}{18\text{x}19\text{x}20}< \frac{1}{4}\)
\(A=1-\frac{1}{2}-\frac{1}{3}+\frac{1}{2}-\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{20}< \frac{1}{4}\)
\(A=1+\left(\frac{1}{2}-\frac{1}{2}\right)+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{4}-\frac{1}{4}\right)+...+\frac{1}{20}< \frac{1}{4}\)
\(A=1+\frac{1}{20}< \frac{1}{4}\)
\(A=\frac{19}{20}< \frac{1}{4}\)
\(A=\frac{19}{20}< \frac{5}{20}\)
\(A>\frac{1}{4}\)
1. Tính tổngfrac{1}{1x2x3}+frac{1}{2x3x4}+frac{1}{3x4x5}+.....+frac{1}{18x19x20}2. Tính nhanhB 1 x 1 + 2 x 2 + 3 x 3 + ......+ 100 x 1003. Tính tổngA 4 + 16 + 36 + 64 +.....+ 100004. Tính tổng:M 1 + 9 + 25 + 49 + 98015. Tính nhanh:left(frac{1}{51}+frac{1}{52}+frac{1}{53}+....+frac{1}{100}right):left(frac{1}{1x2}+frac{1}{3x4}+frac{1}{99x100}right)Nhớ cho mình cách giải nha. Ai làm nhanh, làm đúng sẽ được 10 tick
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1. Tính tổng
\(\frac{1}{1x2x3}+\frac{1}{2x3x4}+\frac{1}{3x4x5}+.....+\frac{1}{18x19x20}\)
2. Tính nhanh
B = 1 x 1 + 2 x 2 + 3 x 3 + ......+ 100 x 100
3. Tính tổng
A = 4 + 16 + 36 + 64 +.....+ 10000
4. Tính tổng:
M = 1 + 9 + 25 + 49 + 9801
5. Tính nhanh:
\(\left(\frac{1}{51}+\frac{1}{52}+\frac{1}{53}+....+\frac{1}{100}\right):\left(\frac{1}{1x2}+\frac{1}{3x4}+\frac{1}{99x100}\right)\)
Nhớ cho mình cách giải nha. Ai làm nhanh, làm đúng sẽ được 10 tick
tính nhanh : 1/1x2x3 + 1/2x3x4 + 1/3x4x5 + ... + 1/18x19x20 ( giúp mình với đg cần gấp)
\(=\dfrac{1}{1\cdot2}-\dfrac{1}{2\cdot3}+\dfrac{1}{2\cdot3}-\dfrac{1}{3\cdot4}+...+\dfrac{1}{18\cdot19}-\dfrac{1}{19\cdot20}\)
=1/2-1/380
=190/380-1/380
=189/380
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tính nhanh : 1/1x2x3 + 1/2x3x4 + 1/3x4x5 + ... + 1/18x19x20 ( giúp mình với đg cần gấp)
Gọi biểu thức trên là S. Ta có :
\(S=\dfrac{1}{1\times2\times3}+\dfrac{1}{2\times3\times4}+\dfrac{1}{3\times4\times5}+...+\dfrac{1}{18\times19\times20}\)
\(=\dfrac{1}{2}\times\left(\dfrac{2}{1\times2\times3}+\dfrac{2}{2\times3\times4}+\dfrac{2}{3\times4\times5}+...+\dfrac{2}{18\times19\times20}\right)\)
Trước tiên, ta áp dụng : \(\dfrac{2}{a\left(a+1\right)\left(a+2\right)}=\dfrac{1}{a\left(a+1\right)}-\dfrac{1}{\left(a+1\right)\left(a+2\right)}\)
Ta sẽ có :
\(S=\dfrac{1}{2}\times\left(\dfrac{1}{1\times2}-\dfrac{1}{2\times3}+\dfrac{1}{2\times3}-\dfrac{1}{3\times4}+\dfrac{1}{3\times4}-\dfrac{1}{4\times5}+...+\dfrac{1}{18\times19}-\dfrac{1}{19\times20}\right)\)
\(=\dfrac{1}{2}\times\left(\dfrac{1}{1\times2}-\dfrac{1}{19\times20}\right)\)
\(=\dfrac{1}{2}\times\dfrac{1}{1\times2}-\dfrac{1}{2}\times\dfrac{1}{19\times20}\)
\(=\dfrac{1}{4}-\dfrac{1}{760}=\dfrac{189}{760}\)
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`=1/2(1/1×2 - 1/2×3 + 1/2×3 - 1/3×4 + 1/3×4 - 1/4×5 + ... + 1/18×19 - 1/19×20)`
`=1/2(1/2 - 1/19×20)`
`=1/2×189/380 `
`=189/760`
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a) Tính hợp lí các tổng sau:
S1: 1/14+1/35+1/65+.....+1/350
S2: 1/3+1/32+1/33+1/34+.....+1/3300
S3:1/1x3x5+1/3x5x7+1/5x7x9+....+1/25x27x29
S4:1+1/2+1/4+1/8+....+1/1024
b) Tìm x biết
(1/1x101+1/2x102+....+1/10x110)x=1/1x11+1/2x12+...+1/100x110
tính nhanh
a) 1-2+3-4+5-6+7 ..............+101-102+103
b)(11x9-100+1):(1x2x3...x10)