b)

program hotrotinhoc;

var s: real;

i,n: byte;

function t(x: byte): longint;

var j: byte;

t1: longint;

begin

t1:=1;

for j:=1 to x do

t1:=t1*j;

t1:=t;

end;

begin

readln(n);

s:=0;

for i:=1 to n do

s:=s+1/t(i);

write(s:1:2);

readln

end.

c) Đề em ghi sai rồi thế này với đúng :

\(T=1+\frac{2}{2^2}+\frac{3}{3^2}+\frac{4}{4^2}+...+\frac{n}{n^2}\)

program hotrotinhoc;

var t: real;

n,i: byte;

begin

readln(n);

t:=0;

for i:=1 to n do

t:=t+i/(i*i);

write(t:1:2);

readln

end.

a)

uses crt;

var N,S,i : integer;

begin clrscr;

S:=1;

for i:= 1 to N do S:=S*i;

writeln('N!=',S);

readln

end.

Các cái kia tương tự :))

d)

program hotrotinhoc;

var i,n: byte;

s: real;

function mu(x: byte): longint;

var j : byte;

k: longint;

begin

k:=1;

for j:=1 to x do

k:=k*x;

k:=mu;

end;

begin

readln(n);

s:=0;

for i:=1 to n do

s:=s+1/mu(i);

write(s:1:2);

readln

end.

e)

program hotrotinhoc;

var s: real;

i,n: byte;

begin

readln(n);

s:=0;

for i:=1 to n do

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

write(s:1:2);

readln

end.

Nguyen svtkvtm Khôi Bùi Nguyễn Việt Lâm Lê Anh Duy Nguyễn Thành Trương DƯƠNG PHAN KHÁNH DƯƠNG An Võ (leo) Ribi Nkok Ngok Bonking ...

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\(a)\) Đặt \(A=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2010^2}\) ta có : 

\(A< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2009.2010}\)

\(A< \frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2009}-\frac{1}{2010}\)

\(A< 1-\frac{1}{2010}=\frac{2009}{2010}< 1\)

\(\Rightarrow\)\(A< 1\) ( đpcm ) 

Vậy \(A< 1\)

Chúc bạn học tốt ~ 

\(1+\frac{1}{n^2}+\frac{1}{\left(n+1\right)^2}=\frac{n^2\left(n+1\right)^2+n^2+\left(n+1\right)^2}{n^2\left(n+1\right)^2}=\frac{n^2\left(n+1\right)^2+2n\left(n+1\right)+1}{n\left(n+1\right)^2}=\frac{\left[n\left(n+1\right)+1\right]^2}{n^2\left(n+1\right)^2}\)

\(\Rightarrow\sqrt{1+\frac{1}{n^2}+\frac{1}{\left(n+1\right)^2}}=\frac{n\left(n+1\right)+1}{n\left(n+1\right)}=1+\frac{1}{n\left(n+1\right)}\)

\(\Rightarrow p=n+\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{n\left(n+1\right)}+\frac{101}{n+1}\)

\(p=n+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{n}-\frac{1}{n+1}+\frac{101}{n+1}\)

\(p=n+1-\frac{1}{n+1}+\frac{101}{n+1}=n+1+\frac{100}{n+1}\ge2\sqrt{\frac{100\left(n+1\right)}{n+1}}=20\)

\(p_{min}=20\) khi \(n+1=\frac{100}{n+1}\Leftrightarrow n=9\)

bạn giải thích cho mình chỗ dấu suy ra thứ 2 được không ạ, vì sao lại xuất hiện n+1/1.2 +......... vậy ạ?

Nguyễn Hồng Nhung

Thay vào công thức:

\(\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}=1+\frac{1}{1.2}\) ; \(\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}=1+\frac{1}{2.3}\) ...

Cộng lại:

\(1+\frac{1}{1.2}+1+\frac{1}{2.3}+...+1+\frac{1}{n\left(n+1\right)}\)

Có n số 1 cộng với nhau ra n

CÒn lại đống \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{n\left(n+1\right)}\) thôi

1) Tính C

\(C=\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+....+\frac{n-1}{n!}\)

\(=\frac{2-1}{2!}+\frac{3-1}{3!}+\frac{4-1}{4!}+...+\frac{n-1}{n!}\)

\(=1-\frac{1}{2!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{3!}-\frac{1}{4!}+...+\frac{1}{\left(n-1\right)!}-\frac{1}{n!}\)

\(=1-\frac{1}{n!}\)

3) a) Ta có : \(P=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{199}-\frac{1}{200}\)

\(=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{199}+\frac{1}{200}-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{200}\right)\)

\(=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{199}+\frac{1}{200}-1-\frac{1}{2}-\frac{1}{3}-...-\frac{1}{100}\)

\(=\frac{1}{101}+\frac{1}{102}+....+\frac{1}{199}+\frac{1}{200}\left(đpcm\right)\)

Thanks !!!