\(1+1+1+1+1+1+1+1+1+1X10=.............\)
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11 tháng 1 2023 lúc 19:04
(1+1/2+1/3+....+1/9+1/10)/ (1/1x10+1/2x9+1/3x8+....+1/8x3+1/9x2+1/10x1)
Tính nhanh
Ta có: \(\frac{1}{1\times10}+\frac{1}{2\times9}+\cdots+\frac{1}{10\times1}\)
\(=2\times\left(\frac{1}{1\times10}+\frac{1}{2\times9}+\cdots+\frac{1}{5\times6}\right)\)
\(=\frac{2}{11}\times\left(\frac{11}{1\times10}+\frac{11}{2\times9}+\cdots+\frac{11}{5\times6}\right)\)
\(=\frac{2}{11}\times\left(1+\frac12+\frac13+\cdots+\frac19+\frac{1}{10}\right)\)
Ta có: \(A=\frac{1+\frac12+\cdots+\frac{1}{10}}{\frac{1}{1\times10}+\frac{1}{2\times9}+\cdots+\frac{1}{9\times2}+\frac{1}{10\times1}}\)
\(=\frac{1+\frac12+\cdots+\frac{1}{10}}{\frac{2}{11}\times\left(1+\frac12+\cdots+\frac{1}{10}\right)}=1:\frac{2}{11}=\frac{11}{2}\)
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11 tháng 1 2023 lúc 18:39
(1+1/2+1/3+....+1/9+1/10)/ (1/1x10+1/2x9+1/3x8+....+1/8x3+1/9x2+1/10x1)
Tính nhanh
1+1-1x1:1x10=?
b=1/1x10+1/2x15+1/3x20+x.......x1/98x495+11/99x500
\(B=\frac{1}{1x2x5}+\frac{1}{2x3x4}+\frac{1}{3x4x5}+...+\frac{1}{98x99x5}+\frac{1}{99x100x5}\)
\(5B=\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{98x99}+\frac{1}{99x100}\)
\(5B=\frac{2-1}{1x2}+\frac{3-2}{2x3}+\frac{4-3}{3x4}+...+\frac{99-98}{98x99}+\frac{100-99}{99x100}\)
\(5B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)
\(5B=1-\frac{1}{100}=\frac{99}{100}\Rightarrow B=\frac{99}{500}\)
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1) 1/1+2 + 1/1+2+3+.........+1/1+2+3+..............+10
2) 1+3+6+10+.........+45+55/1x10+2x9+.......+9x2+10x1
\(A=\dfrac{1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{9}+\dfrac{1}{10}}{\dfrac{1}{1x10}+\dfrac{1}{2x9}+\dfrac{1}{3x8}+...+\dfrac{1}{8x3}+\dfrac{1}{9x2}+\dfrac{1}{10x1}}\)
Ta có: \(\frac{1}{1\times10}+\frac{1}{2\times9}+\cdots+\frac{1}{10\times1}\)
\(=2\times\left(\frac{1}{1\times10}+\frac{1}{2\times9}+\cdots+\frac{1}{5\times6}\right)\)
\(=\frac{2}{11}\times\left(\frac{11}{1\times10}+\frac{11}{2\times9}+\cdots+\frac{11}{5\times6}\right)\)
\(=\frac{2}{11}\times\left(1+\frac12+\frac13+\cdots+\frac19+\frac{1}{10}\right)\)
Ta có: \(A=\frac{1+\frac12+\cdots+\frac{1}{10}}{\frac{1}{1\times10}+\frac{1}{2\times9}+\cdots+\frac{1}{9\times2}+\frac{1}{10\times1}}\)
\(=\frac{1+\frac12+\cdots+\frac{1}{10}}{\frac{2}{11}\times\left(1+\frac12+\cdots+\frac{1}{10}\right)}=1:\frac{2}{11}=\frac{11}{2}\)
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\(\frac{1}{2x3}+\frac{1}{4x5}+\frac{1}{6x7}+\frac{1}{8x9}+\frac{1}{1x10}\)
nhân trước, cộng lại
quy đồng
kết quả là số tìm được
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Tìm hệ số của
1
x
2
trong khai triển
1
−
1
x
10
. A.
1
x
2
B. 2 C. 1 D. -1
Đọc tiếp
Tìm hệ số của 1 x 2 trong khai triển 1 − 1 x 10 .
A. 1 x 2
B. 2
C. 1
D. -1
\(\dfrac{1+3+6+10+...+45+55}{1x10+9x2+3x8+...9x2+10x1}\)
Ta có: \(1+3+6+10+\cdots+45+55\)
\(=\frac12\times\left(2+6+12+20+\cdots+90+110\right)\)
\(=\frac12\times\left(1\times2+2\times3+\cdots+9\times10+10\times11\right)\)
\(=\frac12\times\left\lbrack1\times\left(1+1\right)+2\times\left(2+1\right)+\cdots+10\times\left(10+1\right)\right\rbrack\)
\(=\frac12\times\left\lbrack\left(1\times1+2\times2+\cdots+10\times10\right)+\left(1+2+\cdots+10\right)\right\rbrack\)
\(=\frac12\times\left\lbrack10\times\left(10+1\right)\times\frac{\left(2\times10+1\right)}{6}+10\times\frac{11}{2}\right\rbrack\)
\(=\frac12\times\left\lbrack10\times11\times\frac{21}{6}+5\times11\right\rbrack=\frac12\times\left\lbrack5\times11\times7+5\times11\right\rbrack\)
\(=\frac12\times5\times11\times\left(7+1\right)=\frac{55}{2}\times8=55\times4=220\)
Ta có: \(1\times10+9\times2+\cdots+10\times1\)
\(=2\times\left(1\times10+2\times9+3\times8+4\times7+5\times6\right)\)
\(=2\times\left\lbrack1\times\left(11-1\right)+2\times\left(11-2\right)+3\times\left(11-3\right)+4\times\left(11-4\right)+5\times\left(11-5\right)\right\rbrack\)
\(=2\times\left\lbrack11\times\left(1+2+3+4+5\right)-\left(1\times1+2\times2+3\times3+4\times4+5\times5\right)\right\rbrack\)
\(=2\times\left\lbrack11\times15-\left(1+4+9+16+25\right)\right\rbrack\)
=2x(165-55)
=2x110
=220
Ta có: \(\frac{1\times10+9\times2+\cdots+10\times1}{1+3+6+10+\cdots+45+55}\)
\(=\frac{220}{220}\)
=1
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