Tính tổng
S= (x+\(\frac{1}{x}\))2 + (x2+\(\frac{1}{x^2}\))2+...+(xn+\(\frac{1}{x^n}\))2
T= \(\frac{1}{2}+\frac{3}{2^2}+\frac{5}{2^3}+...+\frac{2n-1}{2^n}\)
Viết chương trình cho phép nhập số tự nhiên N từ bàn phím (với 0<n<=12) rồi thực hiện:
a: Tìm N! = 1.2.3...N
b: tìm S = \(\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+...+\frac{1}{N!}\)
c: T = \(1+\frac{2}{2^2}+\frac{3}{3^2}+\frac{4}{4^2}+...+\frac{1}{n^2}\)
d: S = \(1+\frac{1}{2^2}+\frac{1}{3^3}+\frac{1}{4^4}+...+\frac{1}{n^n}\)
e: \(S_n=\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+...+\frac{n}{n+1}\)
f: S = \(1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+...+\frac{x^n}{n!}\)
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.
S=\(\frac{2n+1}{n-3}+\frac{3n-5}{n-3}-\frac{4n-5}{n-3}\)
a, tìm n để S nhận giá trị nguyên
2 chứng tỏ
\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{99^2}< 1\)
3,tìm số nguyên n,m thỏa mãn
\(\frac{m}{9}-\frac{3}{n}=\frac{1}{18}\)
4 tìm x
\(\frac{1}{1.2}+\frac{1}{1.3}+...+\frac{1}{x\left(x+1\right)}=\frac{6}{7}\)
5,tính nhanh
\(\frac{\left(3.4.2^{16}\right)^2.121^2}{11.2^{13}.4^{11}-16^9}\)
CÁC BẠN GIÚP MÌNH VỚI ,MAI MÌNH PHẢI NỘP RỒI
1/
\(\frac{2n+1}{n-3}+\frac{3n-5}{n-3}-\frac{4n-5}{n-3}=\frac{2n+1+\left(3n-5\right)-\left(4n-5\right)}{n-3}=\frac{2n+1+3n-5-4n+5}{n-3}=\frac{n+1}{n-3}=\frac{n-3+4}{n-3}=\frac{n-3}{n-3}+\frac{4}{n-3}=1+\frac{4}{n-3}\)
Để S là số nguyên <=> n - 3 thuộc Ư(4) = {1;-1;2;-2;4;-4}
n-3 | 1 | -1 | 2 | -2 | 4 | -4 |
n | 4 | 2 | 5 | 1 | 7 | -1 |
Vậy...
2/
Ta có: \(\frac{1}{2^2}< \frac{1}{1.2}=1-\frac{1}{2}\)
\(\frac{1}{3^2}< \frac{1}{2.3}=\frac{1}{2}-\frac{1}{3}\)
...........
\(\frac{1}{99^2}< \frac{1}{98.99}=\frac{1}{98}-\frac{1}{99}\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{99^2}< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}=1-\frac{1}{99}< 1\)
=> ĐPCM
3/
\(\frac{m}{9}-\frac{3}{n}=\frac{1}{18}\)
=> \(\frac{3}{n}=\frac{m}{9}-\frac{1}{18}\)
=> \(\frac{3}{n}=\frac{2m}{18}-\frac{1}{18}\)
=> \(\frac{3}{n}=\frac{2m-1}{18}\)
=> n(2m - 1) = 3.18 = 54
=> n và 2m - 1 thuộc Ư(54) = {1;-1;2;-2;3;-3;6;-6;9;-9;18;-18;27;-27;54;-54}
Mà 2m - 1 là số lẻ => 2m - 1 thuộc {1;-1;3;-3;9;-9;27;-27}
n thuộc {2;-2;6;-6;18;-18;54;-54}
Ta có bảng:
2m - 1 | 1 | -1 | 3 | -3 | 9 | -9 | 27 | -27 |
m | 1 | 0 | 2 | -1 | 5 | -4 | 14 | -13 |
n | 54 | -54 | 18 | -18 | 6 | -6 | 2 | -2 |
Vậy các cặp (m;n) là (1;54) ; (0;-54) ; (2;18) ; (-1;-18) ; (5;6) ; (-4;-6) ; (14;2) ; (-13;-2)
1, Tính \(\frac{1}{2}-\left(\frac{1}{3}+\frac{2}{3}\right)+\left(\frac{1}{4}+\frac{2}{4}+\frac{3}{4}\right)-\left(\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+\frac{4}{5}\right)+...+\left(\frac{1}{100}+\frac{2}{100}+\frac{3}{100}+...+\frac{99}{100}\right)\)2,Tính \(\left(1-\frac{1}{2^2}\right)x\left(1-\frac{1}{3^2}\right)x\left(1-\frac{1}{4^2}\right)x...x\left(1-\frac{1}{n^2}\right)\)
\(\sin^3\frac{x}{3}+3\sin^3\frac{x}{3^2}+...+3^{n-1}\sin^3\frac{x}{3}=\frac{1}{4}\left(3^n\sin^3\frac{x}{3^n}-\sin x\right)\)\(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{2n+1}{2n+2}<\frac{1}{\sqrt{3n+4}}\left(n\ge1\right)\)\(\left(n!\right)^2\ge n^2\ge\left(n+1\right)^{n-1}cho\left(n\ge1\right)\)1.Tìm tất cả các số tự nhiên n thỏa mãn:
\(2.2^2+3.2^3+4.2^4+...+\left(n-1\right)^{2n -1}+n.2^n=8192\)
2. So sánh A và B biết:
\(A=\frac{2011}{1.2}+\frac{2011}{3.4}+\frac{2011}{5.6}+...+\frac{2011}{1999.2000}\)
\(B=\frac{2012}{1001}+\frac{2012}{1002}+\frac{2012}{1003}+...+\frac{2012}{2000}\)
3. Tính \(\left(S-P\right)^{2016}\) biết:\(S=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2013}-\frac{1}{2014}+\frac{1}{2015}\)
\(P=\frac{1}{1008}+\frac{1}{1009}+\frac{1}{1010}+...+\frac{1}{2014}+\frac{1}{2015}\)
4.Tìm x:
a) \(-1\frac{1}{56}:\left(\frac{1}{8}-\frac{1}{7}\right)-\frac{22}{\left|2.x-0,5\right|}=-1\frac{1}{30}:\left(\frac{1}{5}-\frac{1}{6}\right)\)
b) \(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.\frac{5}{12}....\frac{30}{62}.\frac{31}{64}=2^x\)
c) \(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^x\)
Bài 1:Chứng tỏ rằng
a)\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2009.2010}< 1\)
b)\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< 1\)
c)\(\frac{2}{5}< \frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{9^2}< \frac{8}{9}\)
d)\(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}< \frac{3}{16}\)
Bài 2:Cho M=\(\frac{1}{15}+\frac{1}{105}+\frac{1}{315}+..+\frac{1}{9177}\).So sánh với 12
Bài 3:Với giá trị nào của x \(\in\) Z các phân số sau có giá trị là 1 số nguyên
a)A=\(\frac{3}{x-1}\) b)B=\(\frac{x-2}{x+3}\) c)C=\(\frac{2x+1}{x-3}\) d)D=\(\frac{x^2-1}{x+1}\)
Bài 4:a) Chứng tỏ rằng các phân số sau tối giản với mọi số tự nhiên n
a)\(\frac{n+1}{2n+3}\) b)\(\frac{2n+3}{4n+8}\)
Mình đang cần gấp lắm ,làm ơn
Tìm x
\(\frac{-3}{29}+\frac{-7}{29}\le\frac{x}{29}\le\frac{-3}{29}-\frac{5}{29}\)
Tìm \(n\in Z\)để \(\frac{n^2+n-5}{n+2}\)là số nguyên
Tính \(S=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+......+\frac{1}{2^{99}}+\frac{1}{2^{100}}\)
\(1,-\frac{3}{29}+\frac{-7}{29}\le\frac{x}{29}\le-\frac{3}{29}-\frac{5}{29}\)
\(\Rightarrow-\frac{10}{29}\le\frac{x}{29}\le-\frac{8}{29}\Rightarrow-10\le x\le-8\)
\(\Rightarrow x=\left\{-8;-9;-10\right\}\)
\(S=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{99}}+\frac{1}{2^{100}}\)
\(\Rightarrow2S=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{99}}\)
\(S=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{99}}+\frac{1}{2^{100}}\)
\(\Rightarrow2S-S=S=1-\frac{1}{2^{100}}\)
Bài 1:
1. Tính: \(E=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+4\right)+...+\frac{1}{200}\left(1+2+...+200\right)\)
2. Tìm và tính tổng các số nguyên x thỏa mãn: \(\frac{21}{5}\left|x\right|< 2019\)
3. Tìm x, biết: \(\frac{2^{24}\left(x-3\right)}{\left(3\frac{5}{7}-1,4\right)\left(6\cdot2^{24}-4^{13}\right)}=\left(\frac{5}{3}\right)^2\)
\(1+2+...+n=\frac{n\left(n+1\right)}{2}\)
\(\Rightarrow E=1+\frac{1}{2}\frac{2.3}{2}+\frac{1}{3}.\frac{3.4}{2}+\frac{1}{4}.\frac{4.5}{2}+...+\frac{1}{200}.\frac{200.201}{2}\)
\(=1+\frac{1}{2}\left(3+4+5+...+201\right)\)
\(=1+\frac{1}{2}\left(1+2+3+...+201-1-2\right)\)
\(=1+\frac{1}{2}\left(\frac{201.202}{2}-3\right)=10150\)
\(\frac{21}{5}\left|x\right|< 2019\Rightarrow\left|x\right|< 2019\div\frac{21}{5}=\frac{3365}{7}\)
\(\Rightarrow-480\le x\le480\)
\(\Rightarrow\sum x=-480+480-479+479+...+-1+1+0=0\)
\(\frac{2^{24}\left(x-3\right)}{\frac{81}{35}.\left(6.2^{24}-2^{26}\right)}=\frac{25}{9}\)
\(\Leftrightarrow\frac{2^{24}\left(x-3\right)}{2^{24}\left(6-2^2\right)}=\frac{25}{9}.\frac{81}{35}\)
\(\Leftrightarrow\frac{x-3}{2}=\frac{45}{7}\)
\(\Leftrightarrow x-3=\frac{90}{7}\)
\(\Rightarrow x=\frac{111}{7}\)