1/a,

-Ta có: 

$B<1\Leftrightarrow B<\frac{10^{2005}+1+9}{10^{2006}+1+9}=\frac{10^{2005}+10}{10^{2006}+10}=\frac{10(10^{2004}+1)}{10(10^{2005}+1)}=\frac{10^{2004}+1}{10^{2005}+1}=A$

-Vậy: B<A

b,$A=1+(\frac{1}{2})^2+...+(\frac{1}{100})^2$

$\Leftrightarrow A=1+\frac{1}{2^2}+...+\frac{1}{100^2}$

$\Leftrightarrow A<1+\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}$

$\Leftrightarrow A<1+\frac{1}{1}-\frac{1}{2}+...+\frac{1}{99}-\frac{1}{100}$

$\Leftrightarrow A<1+1-\frac{1}{100}\Leftrightarrow A<2-\frac{1}{100}\Leftrightarrow A<2(đpcm)$
2,
a.
-Ta có:$\Rightarrow \frac{3x+7}{x-1}=\frac{3(x-1)+16}{x-1}=\frac{3(x-1)}{x-1}+\frac{16}{x-1}=3+\frac{16}{x-1}
-Để: 3x+7/x-1 nguyên
-Thì: $\frac{16}{x-1}$ nguyên
$\Rightarrow 16\vdots x-1\Leftrightarrow x-1\in Ư(16)\Leftrightarrow ....$
b, -Ta có:
$\frac{n-2}{n+5}=\frac{n+5-7}{n+5}=1-\frac{7}{n+5}$
-Để: n-2/n+5 nguyên
-Thì: \frac{7}{n+5} nguyên
$\Leftrightarrow 7\vdots n+5\Leftrightarrow n+5\in Ư(7)\Leftrightarrow ...$

Để đánh số trang một quyển sách dày 295 trang cần dùng bao nhiêu chữ số?

a:

#include <bits/stdc++.h>

using namespace std;

long long i,n,s;

int main()

{

cin>>n;

s=0;

for (i=1; i<=n; i++) s=s+i;

cout<<s;

return 0;

}

Program HOC24;

var i,n,s: byte;

begin

write('Nhap N: '); readln(n);

s:=0;

for i:=1 to n do s:=s+i;

write('S = ',s);

readln

end.

2:

#include <bits/stdc++.h>

using namespace std;

int A[100],ln,nn,vt1,vt2,n;

int main()

{

cin>>n;

for(int i=1; i<=n; i++) cin>>A[i];

ln=A[1];

for (int i=1; i<=n; i++)

ln=max(ln,A[i]);

nn=A[1];

for (int i=1; i<=n; i++)

nn=min(nn,A[i]);

vt1=1; vt2=n;

for (int i=1; i<=n; i++)

if (ln==A[i] && vt1<=i) vt1=i;

for (int i=n; i>=1; i--)

if (nn==A[i] && vt2>=i) vt2=i;

swap(A[vt1],A[vt2]);

for (int i=1; i<=n; i++)

cout<<A[i]<<" ";

}