a)xét ΔBAD và ΔBCE có

\(\widehat{ADB}=\widehat{CEB}=90^o\)

\(\widehat{ABC}\) là góc chung

AB=BC(ΔABC cân tại B)

⇒ ΔBAD=ΔBCE(c.huyền.g.nhọn)

b)xét ΔEBF và ΔDBF có:

BF là cạnh chung

BD=BE(ΔBAD=ΔBCE)

\(\widehat{BDF}=\widehat{BEF}=90^o\)

⇒ΔEBF=ΔDBF(c.huyền.c.g.vuông)

⇒\(\widehat{EBF}=\widehat{DBF}\)(2 góc tương ứng)

hay BF là phân giác của \(\widehat{ABC}\)(đ.p.cm)

c)xét ΔABF và ΔCBF có:

AC=BC(ΔABC cân tại B)

BF là cạnh chung

\(\widehat{EBF}=\widehat{DBF}\)(ΔEBF=ΔDBF)

⇒ΔABF=ΔCBF(c-g-c)

⇒FA=FC(2 cạnh tương ứng)

xét ΔAFC có:

FA+FC>AC(bất đẳng thức tam giác)

mà FA=FC⇒FA>\(\dfrac{AC}{2}\)(đ.p.cm)

program tinh_tong;

uses crt;

var i,n:integer;

s:real;

begin

clrscr;

write('nhap n:');readln(n);

i:=1;

while i<=n*2-1 do

begin

s:=s+1/i;

i:=i+2;

end;

writeln('tong la: ',s);

readln;

end.

program tinh_tong;

uses crt;

var i,n:integer;

s:real;

begin

clrscr;

write('nhap n:');readln(n);

for i:=1 to n*2-1 do

if i mod 2=1 then s:=s+1/i;

writeln('tong la: ',s);

readln;

end.

Program Xoa_mang;

uses crt;

var m:array[1..100] of integer;

n,i,k:byte;

begin

Write(‘So phan tu cua day: ‘);readln(n);

for i:=1 to n do

Begin

write(‘M[‘,i,’]=’);

readln(M[i]);

end;

write(‘Nhap phan tu can xoa: ‘);readln(k);

for i:=k to n-1 do m[i]:=m[i+1];

for i:=1 to n-1 do write(m[i],’  ‘);

readln

end.

Program Xoa_mang;

uses crt;

var m:array[1..100] of integer;

n,i,k:byte;

begin

Write(‘So phan tu cua day: ‘);readln(n);

for i:=1 to n do

Begin

write(‘M[‘,i,’]=’);

readln(M[i]);

end;

write(‘Nhap phan tu can xoa: ‘);readln(k);

for i:=k to n-1 do m[i]:=m[i+1];

for i:=1 to n-1 do write(m[i],’  ‘);

readln

end.

b)

program fibonaci;

uses crt;

var i,n:integer;

a:array[1..30]of integer;

begin

clrscr;

repeat

write('nhap n:');readln(n);

if (n<1)or(n>30) then writeln('so n phai lon hon hoac bang 1 va nho hon hoac bang 30:);

until (n>=1)and(n<=30);

a[1]:=1;

a[2]:=1;

for i:=3 to n do

a[i]:=a[i-1]+a[i-2];

writeln(n,' so fibonaci dau tien la:');

for i:=1 to n do

write(a[i]:3);

readln;

end.

a)

program UCLN_va_BCNN;

uses crt;

var a,b,c,r,p:integer;

begin

clrscr;

write('nhap a,b:');readln(a,b);

if a<b then 

begin

c:=a;

a:=b;

b:=c;

end;

p:=a*b;

r:=a mod b;

while r<>0 do

begin

a:=b;

b:=r;

r:=a mod b;

end;

writeln('UCLN la: ',b);

writeln('BCNN la: ',p div b);

readln;

end.

program tong_while_do;

uses crt;

var i,n:integer;

t:real;

begin

clrscr;

write('nhap n:');readln(n);

t:=0;i:=3;

while i<=3*n do

begin

t:=t+1/i;

i:=i+3;

end;

writeln('tong la: ',t);

readln;

end.