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9 tháng 3 2018
hahaha
9 tháng 3 2018

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{n\left(n+1\right)}=\frac{2013}{2014}\)

\(\Rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{n}-\frac{1}{n+1}=\frac{2013}{2014}\)

\(\Rightarrow1-\frac{1}{n+1}=\frac{2013}{2014}\)

\(\Rightarrow\frac{1}{n+1}=1-\frac{2013}{2014}\)

\(\Rightarrow\frac{1}{n+1}=\frac{1}{2014}\)

\(\Rightarrow n+1=2014\)

\(\Rightarrow n=2014-1\)

\(\Rightarrow n=2013\)

28 tháng 5 2020

program tinhtoan;

uses crt;

var: i;n:interger;

S:real;

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

S:=0;

For i:=1 to n*(n*1) do S:=S+\(\frac{1}{i};\)

writeln(' S=',S);

End.

(ps: ko chắc )

6 tháng 6 2017

a,\(x^3-7x+6\)

\(=x^3-2x^2+2x^2-4x-3x+6\)

\(=\left(x^3-2x^2\right)+\left(2x^2-4x\right)-\left(3x-6\right)\)

\(=x^2.\left(x-2\right)+2x.\left(x-2\right)-3.\left(x-2\right)\)

\(=\left(x-2\right).\left(x^2+2x-3\right)\)

\(=\left(x-2\right).\left(x^2-x+3x-3\right)\)

\(=\left(x-2\right).\left[\left(x^2-x\right)+\left(3x-3\right)\right]\)

\(=\left(x-2\right).\left[x.\left(x-1\right)+3.\left(x-1\right)\right]\)

\(=\left(x-2\right).\left(x-1\right).\left(x+3\right)\)

b,\(x^3-9x^2+6x+16\)

\(=x^3-8x^2-x^2+8x-2x+16\)

\(=\left(x^3-8x^2\right)-\left(x^2-8x\right)-\left(2x-16\right)\)

\(=x^2.\left(x-8\right)-x.\left(x-8\right)-2.\left(x-8\right)\)

\(=\left(x-8\right).\left(x^2-x-2\right)\)

\(=\left(x-8\right).\left(x^2+x-2x-2\right)\)

\(=\left(x-8\right).\left[\left(x^2+x\right)-\left(2x+2\right)\right]\)

\(=\left(x-8\right).\left[x.\left(x+1\right)-2.\left(x+1\right)\right]\)

\(=\left(x-8\right).\left(x+1\right).\left(x-2\right)\)

c,\(x^3-6x^2-x+30\)

\(=x^3-5x^2-x^2+5x-6x+30\)

\(=\left(x^3-5x^2\right)-\left(x^2-5x\right)-\left(6x-30\right)\)

\(=x^2.\left(x-5\right)-x.\left(x-5\right)-6.\left(x-5\right)\)

\(=\left(x-5\right).\left(x^2-x-6\right)\)

\(=\left(x-5\right).\left(x^2+2x-3x-6\right)\)

\(=\left(x-5\right).\left[\left(x^2+2x\right)-\left(3x+6\right)\right]\)

\(=\left(x-5\right).\left[x.\left(x+2\right)-3.\left(x+2\right)\right]\)

\(=\left(x-5\right).\left(x+2\right).\left(x-3\right)\)

Chúc bạn học tốt!!!

6 tháng 6 2017

d,\(2x^3-x^2+5x+3\)

\(=2x^3+x^2-2x^2-x+6x+3\)

\(=\left(2x^3+x^2\right)-\left(2x^2+x\right)+\left(6x+3\right)\)

\(=x^2.\left(2x+1\right)-x.\left(2x+1\right)+3.\left(2x+1\right)\)

\(=\left(2x+1\right).\left(x^2-x+3\right)\)

e, \(27x^3-27x^2+18x-4\)

\(=27x^3-9x^2-18x^2+6x+12x-4\)

\(=\left(27x^2-9x^2\right)-\left(18x^2-6x\right)+\left(12x-4\right)\)

\(=9x^2.\left(3x-1\right)-6x.\left(3x-1\right)+4.\left(3x-1\right)\)

\(=\left(3x-1\right).\left(9x^2-6x+4\right)\)

Chúc bạn học tốt!!!

3 tháng 11 2017

1. Đề bài ko đúng, cô lấy x = 1, y = 2 thì:

\(VT=1-\frac{1.4}{3}=-\frac{1}{3}\)

\(VP=1-1.2=-1\)

Ta thấy VT và VP không bằng nhau.

2. Ta có thể thực hiện phép chia f(x) cho g(x) hoặc tách như sau:

\(f\left(x\right)=x^{2013}+x^{2012}-kx^5-kx^4+kx^4+kx^3+\left(1-k\right)x^3+\left(1-k\right)x^2+kx^2+kx\)

\(-kx-k-2k\)

\(=\left(x+1\right)\left[x^{2012}-kx^4+kx^3+\left(1-k\right)x^2+kx-k\right]-2k\)

\(=g\left(x\right)\left[x^{2012}-kx^4+kx^3+\left(1-k\right)x^2+kx-k\right]-2k\)

Vậy để f(x) chia g(x) dư 2014 thì -2k = 2014 hay k = -1007