Program HOC24;

var b: real;

i,n: integer;

begin

write('Nhap n='); readln(n);

b:=0;

for i:=1 to n do b:=b+1/(i+2);

write('B= ',b:1:2);

readln

end.

Sửa lại đề bài : \(A=....+\dfrac{1}{n\left(n+2\right)}\)

Program HOC24;

var i,n: integer;

a: real;

begin

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

a:=0;

for i:=1 to n do a:=a+1/(n*(n+2));

write('A = ',a:6:2);

readln

end.

uses crt;

var i,n:integer; S:real;

Begin

clrscr;

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

for i:=1 to n do S:=S+1/(i*(i+2));

writeln('Tong la: ',S:3:1);

readln

End.

Mô tả tính tổng:

-B1:A\(\leftarrow0\),i\(\leftarrow1.\)

-B2:A\(\leftarrow\dfrac{1}{i\times\left(i+2\right)}\)

-B3:\(i\leftarrow i+1\)

-B4:Nếu \(i\le n\),quay lại B2

-B5:Ghi kết quảA và kết thúc thuật toán.

Giải thuật tính tổng trên là :


- Bước 1:Nhập số n



- Bước 2:S<-0; i<-0;



- Bước 3:i<-i+1;


- Bước 4:Nếu i <= n thì S:=S+1/(i*(i+2)) nghĩa là công vào S = S+1/(i*(i+2)) và quay lại

- Bước 5.Ngược lại thông báo kết quả và kết thúc thuật toán.

program bai1;

var n,s,i:longint;

begin

write('N= ');realn(n);

s:=0;

for i:=1to n do

s:=s+1/n*(n+2);

write('S= ',s);

readln

end.

uses crt;

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

i,n,d:integer;

begin

clrscr;

repeat

writeln('nhap n=');readln(n);

until n>0;

for i:=1 to n do

begin writeln('b[',i,']','=');readln(b[i]);end;

writeln('so cac so le la');

for i:=1 to n do

if b[i] mod 2<>0 then d:=d+1;

writeln(d);readln;end.

uses crt;

var n,i:longint; s:real;

begin

clrscr;

s:=0;

writeln('nhap vao n=');readln(n);

writeln('tong cua A la');

for i:=1 to n do

s:=s + 1/(i*(i+2));

writeln(s:4:3);readln;end.

\(A=\dfrac{1}{2}\left(2.\dfrac{2}{3}\right)\left(\dfrac{3}{2}.\dfrac{3}{4}\right)\left(\dfrac{4}{3}.\dfrac{4}{5}\right)....\left(\dfrac{2016}{2015}.\dfrac{2016}{2017}\right)\)

\(=\dfrac{2016}{2017}\)

\(\left(1+\dfrac{1}{1.3}\right).\left(1+\dfrac{1}{2.4}\right).\left(1+\dfrac{1}{3.5}\right).........\left[1+\dfrac{1}{x.\left(x+2\right)}\right]=\dfrac{31}{16}\)

\(\Rightarrow\dfrac{2^2}{1.3}.\dfrac{3^2}{2.4}.\dfrac{4^2}{3.5}........\dfrac{\left(x+1\right)^2}{x.\left(x+2\right)}=\dfrac{31}{16}\)

\(\Rightarrow\dfrac{\left[2.3.4.............\left(x+1\right)\right].\left[2.3.4.............\left(x+1\right)\right]}{\left(1.2.3...................x\right).\left(3.4.5..........................\left(x+2\right)\right)}=\dfrac{31}{16}\)

\(\Rightarrow\dfrac{\left(x+1\right).2}{1.\left(x+2\right)}=\dfrac{31}{16}\)

\(\Leftrightarrow16.2\left(x+1\right)=31.\left(x+2\right)\)

\(\Rightarrow32x+32=31x+62\)

\(\Rightarrow x=30\)

Vậy x=30

Chúc bn học tốt

ĐKXĐ: \(x\notin\left\{0;-2\right\}\)

Ta có: \(\left(1+\dfrac{1}{1\cdot3}\right)\left(1+\dfrac{1}{2\cdot4}\right)\left(1+\dfrac{1}{3\cdot5}\right)\cdot...\cdot\left(1+\dfrac{1}{x\left(x+2\right)}\right)=\dfrac{31}{16}\)

\(\Leftrightarrow\dfrac{1\cdot3+1}{1\cdot3}+\dfrac{1+2\cdot4}{2\cdot4}+\dfrac{1+3\cdot5}{3\cdot5}\cdot...\cdot\dfrac{1+x\left(x+2\right)}{x\left(x+2\right)}=\dfrac{31}{16}\)

\(\Leftrightarrow\dfrac{2\cdot2}{1\cdot3}+\dfrac{3\cdot3}{2\cdot4}+\dfrac{4\cdot4}{3\cdot5}+...+\dfrac{\left(x+1\right)\left(x+1\right)}{x\left(x+2\right)}=\dfrac{31}{16}\)

\(\Leftrightarrow\dfrac{1\cdot2\cdot3\cdot...\cdot\left(x+1\right)}{1\cdot2\cdot3\cdot...\cdot x}\cdot\dfrac{2\cdot3\cdot4\cdot...\cdot\left(x+1\right)}{3\cdot4\cdot5\cdot...\cdot\left(x+2\right)}=\dfrac{31}{16}\)

\(\Leftrightarrow\left(x+1\right)\cdot\dfrac{2}{x+2}=\dfrac{31}{16}\)

\(\Leftrightarrow\dfrac{2x+2}{x+2}=\dfrac{31}{16}\)

\(\Leftrightarrow\dfrac{32x+32}{16\left(x+2\right)}=\dfrac{31\left(x+2\right)}{16\left(x+2\right)}\)

Suy ra: \(32x+32=31x+62\)

\(\Leftrightarrow x=30\)(thỏa ĐK)

Vậy: S={30}

\(A=\dfrac{1}{2}.\left(1+\dfrac{1}{1.3}\right)\left(1+\dfrac{1}{2.4}\right)\left(1+\dfrac{1}{3.5}\right)....\left(\dfrac{1}{2015.2017}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{2}{1}.\dfrac{2}{3}\right).\left(\dfrac{3}{2}.\dfrac{3}{4}\right).\left(\dfrac{4}{3}.\dfrac{4}{5}\right)....\left(\dfrac{2016}{2015}.\dfrac{2016}{2017}\right)\)

\(=\dfrac{1}{2}.\left(\dfrac{2}{1}.\dfrac{2}{3}\right).\left(\dfrac{3}{2}.\dfrac{3}{4}\right).\left(\dfrac{4}{3}.\dfrac{4}{5}\right).....\left(\dfrac{2016}{2015}.\dfrac{2016}{2017}\right)\)

\(=\dfrac{2016}{2017}\)