10 + 10 =.................
ai giúp mình với
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\(1-\left(\frac{2}{5}+\frac{1}{10}\right)=1-\left(\frac{4}{10}+\frac{1}{10}\right)=1-\frac{1}{2}=\frac{1}{2}\)
1. What has Jim recently experienced ?
2. where do the ethnic minorities in Viet Nam often live ?
3. How are their costumes ?
4. Where do they often gather in special occasions ?
5. What does the chief of the community often tell at the communal house ?
6. When do ethnic people often hold festival ?
Lời giải:
Ta có:
$10\equiv -1\pmod {11}$
$\Rightarrow 10^{2022}\equiv (-1)^{2022}\equiv 1\pmod {11}$
$\Rightarrow A=10^{2022}-1\equiv 1-1\equiv 0\pmod {11}$
Vậy $A\vdots 11$
ok
A= 10^2022-1
Ta có thể thấy 10^2022=100000000...........0000000000
10000000.......0000000000-1 thì lúc nnày tổng bằng
9999999999999999........................999999999999999999999
mà 99999999999999999999999....................9999999999999999999chia hết cho 11 nên tổng này chia hết cho 11
a: \(\frac{-2x+3}{5xy}+\frac{3x-4}{5xy}\)
\(=\frac{-2x+3+3x-4}{5xy}=\frac{x-1}{5xy}\)
b: \(\frac{x\left(x-2\right)}{x-3}+\frac{3}{3-x}\)
\(=\frac{x^2-2x-3}{x-3}\)
\(=\frac{\left(x-3\right)\left(x+1\right)}{x-3}=x+1\)
c: \(\frac{2x+7}{3\left(x+2\right)}-\frac{x+5}{3\left(x+2\right)}\)
\(=\frac{2x+7-x-5}{3\left(x+2\right)}\)
\(=\frac{x+2}{3\left(x+2\right)}=\frac13\)
d: \(\frac{5}{2x+6}+\frac{3}{x^2-9}\)
\(=\frac{5}{2\left(x+3\right)}+\frac{3}{\left(x-3\right)\left(x+3\right)}\)
\(=\frac{5\left(x-3\right)+6}{2\left(x-3\right)\left(x+3\right)}=\frac{5x-9}{2\left(x-3\right)\left(x+3\right)}\)
e: \(\frac{3x}{x+2}+\frac{x+3}{x^2-4}\)
\(=\frac{3x\left(x-2\right)+x+3}{\left(x-2\right)\left(x+2\right)}=\frac{3x^2-6x+x+3}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{3x^2-5x+3}{\left(x-2\right)\left(x+2\right)}\)
f: \(\frac{3x+2}{\left(x+2\right)^2}-\frac{1}{x+2}\)
\(=\frac{3x+2-\left(x+2\right)}{\left(x+2\right)^2}=\frac{2x}{\left(x+2\right)^2}\)
\(\frac{9}{10!}+\frac{10}{11!}+...+\frac{999}{1000!}\)
= \(\frac{1}{9!}-\frac{1}{10!}+\frac{1}{10!}-\frac{1}{11!}+...+\frac{1}{999!}-\frac{1}{100!}\)
= \(\frac{1}{9!}-\frac{1}{1000!}\)< \(\frac{1}{9!}\)( dpcm )
A = 9/10! + 9/11! + 9/12! + ...... + 9/1000! < 9/10! + 10/11! + 11/12! + ... + 999/1000! = B
9/10! = 1/9! - 1/10!
10/11! = 1/10! - 1/11!
...
999/1000! = 1/999! - 1/1000!
=> B = 1/9! - 1/1000! < 1/9!
=> A < 1/9! (dpcm)
10+10=20
10+10=20