Ta có 1.4/2.3=(2-1)(3+1)/2.3=1-1/2+1/3-1/2.3
2.5/3.4=(3-1)(4+1)/3.4=1-1/3+1/4-1/3.4
...
Suy ra N=(1-1/2+1/3-1/2.3)+(1-1/3+1/4-1/3.4)+....+(1-1/99+1/100-1/99.100)
N=98+1/100−1/2−1/2.3−1/3.4−....−1/99.100
Xét P=1/2.3+1/3.4+....+1/99.100
P= 1/2−1/3+1/3−1/4+.....+1/99−1100
P=1/2−1/100
Vậy N=98-1+1/50
N=97+1/50
Vậy 97<N<98(ĐPCM)
Cho \(N=\frac{1.4}{2.3}+\frac{2.5}{3.4}+\frac{3.6}{4.5}+...+\frac{98.101}{99.100}\)
Chứng minh : 97 < N < 98
Cho \(N=\frac{1.4}{2.3}+\frac{2.5}{3.4}+\frac{3.6}{4.5}+...+\frac{98.101}{99.100}\)
Chứng minh : 97 < N < 98
a)CHO A = \(\frac{2}{3^2}\)+ \(\frac{2}{5^2}\) + \(\frac{2}{7^2}\)+.........+ \(\frac{2}{2007^2}\)
CHỨNG MINH RẰNG: A < \(\frac{1003}{2008}\)
b)CHO N = \(\frac{1.4}{2.3}\)+ \(\frac{2.5}{3.4}\)+ \(\frac{3.6}{4.5}\)+.........+ \(\frac{98.101}{99.100}\)
CHỨNG MINH RẰNG: 97 < N < 98
~ giúp mk với~
\(A=\frac{1.4}{2.3}+\frac{2.5}{3.4}+...+\frac{98.101}{99.100}\) CMR:97<A<98
TÍNH N=\(\frac{1.4}{2.3}+\frac{2.5}{3.4}+...+\frac{98.101}{99.100}\)
biết a = 1.2+2.3+3.4+.....+99.100=333300 thì B = 1.4+2.5+3.6+....+99.102=......
biết A = 1.2+2.3+3.4+.........+99.100=333300 thì B = 1.4+2.5+3.6+......+99.102 = .....
Biết A=1.2+2.3+3.4......+99.100=333300 thì B=1.4+2.5+3.6..+99.102= ?
Biết A=1.2+2.3+3.4+...+99.100=333300 thì B=1.4+2.5+3.6+...+ 99.102=?
