\(S=\dfrac{1}{2^2}+\dfrac{1}{\left(2.2\right)^2}+\dfrac{1}{\left(2.3\right)^2}+...+\dfrac{1}{\left(2.10\right)^2}\)

\(=\dfrac{1}{2^2}+\dfrac{1}{2^2.2^2}+\dfrac{1}{2^2.3^2}+...+\dfrac{1}{2^2.10^2}\)

\(=\dfrac{1}{2^2}\left(1+\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{10^2}\right)\)

\(< \dfrac{1}{2^2}\left(1+\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{9.10}\right)\)

\(=\dfrac{1}{4}\left(1+1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\)

\(=\dfrac{1}{4}\left(2-\dfrac{1}{10}\right)< \dfrac{1}{4}.2=\dfrac{1}{2}\) (đpcm)

d

D

D

const fi='kt.txt'

fo='kq.out'

var f1,f2:text;

s:string;

i,dem,d:integer;

begin

assign(f1,fi); reset(f1);

assign(f2,fo); rewrite(f2);

readln(f1,s);

d:=length(s);

dem:=0;

for i:=1 to d do 

 if s[i]='e' then inc(dem);

writeln(f2,dem);

close(f1);

close(f2);

end.

\(3,8276< \overline{3,8ab5}< 3,836\)

=>\(276< \overline{ab5}< 360\)

=>\(\left(a,b\right)\in\left\{\left(2;8\right);\left(2;9\right);\left(3;0\right);\left(3;1\right);\left(3;2\right);\left(3;3\right);\left(3;4\right);\left(3;5\right)\right\}\)

\(\left(2x-3,5\right)^2+\left(x^2-\dfrac{49}{16}\right)^2=0\)

Vì \(\left(2x-3,5\right)^2\ge0;\left(x^2-\dfrac{49}{16}\right)^2\ge0\)

\(\Rightarrow\left(2x-3,5\right)^2+\left(x^2-\dfrac{49}{16}\right)^2\ge0\)

Mà \(\left(2x-3,5\right)^2+\left(x^2-\dfrac{49}{16}\right)^2=0\)

\(\Rightarrow\left\{{}\begin{matrix}2x-3,5=0\\x^2-\dfrac{49}{16}=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\dfrac{7}{4}\\x=\pm\dfrac{7}{4}\end{matrix}\right.\Rightarrow x=\dfrac{7}{4}\)

A

A

Đáp án A

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