Tính :
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 . 0 + 1 = ?
Chứng minh
a, 1/4+1/16+1/36+1/64+1/100+1/144+1/196<1/2
b, 11/15<1/21+1/22+1/23+...+1/59+1/60<3/2
A= (1-1/4).(1-1/9).(1-1/16).....(1-1/100)
Rút gọn biểu thức:
R=(1/2+1).(1/3+1).(1/4+1)....(1/98+1).(1/99+1)
Chứng minh rằng: A = 1/4+1/16+1/36+1/64+1/100+1/144+1/196+1/256+1/324<1/2
(1-1/2)x(1-1/3)x(1-1/4)...(1-1/999)
1/2011x =(1-1/2)(1-1/3)(1-1/4)
rút gọn B = ( 1 - 1/2 ) x ( 1 -1/3 ) x ( 1 - 1/4 ) .... ( 1 -1/20 )
Tính nhanh \(1\frac{1}{2}.1\frac{1}{3}.1\frac{1}{4}.1\frac{1}{5}...1\frac{1}{999}\)
A=1-1/2+1/3-1/4+1/5-1/6+....+1/49-1/50. Chứng minh rằngA<5/6