1. So sanh voi1/2:
a) A= 1/9+ 1/16+ 1/25+......+ 1/3600.
b) So sanh voi 2/5:
S = 1/7 + 1/13 + 1/21 + 1/31 + 1/43 + 1/57 + 1/73+ 1/91
Bài 1: Chứng minh rằng
1/3+1/7+1/13+1/21+1/31+1/43+1/57+1/73+1/91<1
Bài 2: So sánh với 1
1/4+1/9+1/16+1/25+....+1/10000
Bài 1: CMR:1/3+1/7+1/13+1/21+1/31+1/43+1/57+1/73+1/91<1
Giải
Ta đặt M=1/3+1/7+1/13+1/21+1/31+1/43+1/57+1/73+1/91
Vậy M<1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
M< 1/2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10
M< (1-1/2) +(1/2-1/3) +(1/3-1/4) +(1/4-1/5) +(1/5-1/6) +(1/6-1/7) +(1/7-1/8) +(1/8-1/9) +(1/9-1/10)
M< 1-1/10 < 9/10 (1)
Vì 9/10 < 1 (2)
Từ(1) và (2) ta có : 1/3+1/7+1/13+1/21+1/31+1/43+1/57+1/73+1/91<1
Bài 2:So sánh với 1: 1/4+1/9+1/16 + 1/25 +...+1/10000
Giải
Ta đặt M =1/4+1/9+1/16 + 1/25 +...+1/10000
Hay M = 1/2X2+ 1/3X3+1/4X4+1/5X5 +...+1/100X100
M< 1/1x2+ 1/2x3+1/3x4+1/4x5+...+1/99x100
M< (1-1/2) +(1/2-1/3) +(1/3-1/4) +(1/4-1/5)+...+(1/99-1/100)
M< 1-1/100 < 99/100 (1)
Vì 99/100 < 1 (2)
Từ(1) và (2) ta có : 1/4+1/9+1/16 + 1/25 +...+1/10000 <1
cho A=1+1/2+1/3+1/4+......+1/4026, B=1+1/3+1/5+1/7+...+1/4025 so sanh a/b voi1+2013/2014
Cho A = 1/5 + 1/6 + 1/7 + 1/8 + 1/9.
Khong thuc hien phep ting , hay so sanh gia tri cua A voi1
vì các ps trên đều bé hơn1 nên 0 cần thực hiện phép thính cũng biết đáp án < 1
cho a=1+1\2...+z\4026,b=1+1/3+1/5+...+1/4025 so sanh a\b voi1\2013\2014
cho A=1/4+1/9+1/16+1/25+...+1/10000 so sanh A voi 3/4
cho a=(1-1/2)*(1-1/3)*(1-1/4)*...(1-1/19)*(1-1/20)
b=(1-1/4)*(1-1/9)*(1-1/16)*...*(1-1/18)*(1-1/180)
so sanh a va 1/21
so sanh b va 11/21
Cho A=1/2!+2/3!+......+8/9!+9/10!.so sanh A voi1.Voi n!=1.2.3.....n(tich cua n so tu nhien khac 0 dau tien)
So sanh 1/4+1/9+1/16+1/25+1/36+...+1/10000 voi 1 va neu cach giai(so sanh) nua nhe!
\(\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+.....+\frac{1}{10000}=\frac{1}{2.2}+\frac{1}{3.3}+\frac{1}{4.4}+.....+\frac{1}{100.100}\)
\(\frac{1}{2.2}+\frac{1}{3.3}+\frac{1}{4.4}+....+\frac{1}{100.100}<\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{99.100}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-....-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)\(=1-\frac{1}{100}=\frac{99}{100}<1\)
Vậy \(\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+.....+\frac{1}{10000}<1\)
(1/4-1).(1/9-1).....91/400-1) so sanh voi -1/2