hình như phân số cuối phải là 1/324
nếu là 1/324 thì tớ giải nè:
A = 1/4+1/16+1/36+1/64+1/100+1/144+1/196+1/256+1/324
= 1/4.(1+1/2^2+1/3^2+1/4^2+1/5^2+1/6^2+1/7^2+1/8^2+1/9^2) <1/4.(1+1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9)
= 1/4.(1+1-1/9)
= 1/4.17/9 = 17/36<18/36 = 1/2
=> A = 1/4+1/16+1/36+1/64+1/100+1/144+1/196+1/256+1/324<1/2
A<1/1*2+1/3*4+........+1/17*18
A<1-1/2+1/3-1/4+.......+1/17-1/18
A<(1+1/3+.....+1/17)-(1/2+1/4+......+1/18)
A<(1+1/2+1/3+......+1/18)-(1/2+1/4+.....+1/18)-(1/2+1/4+.......+1/18)
A<1-1/18-(1/2+1/3+1/4+......+1/17)
A<17/18-1/2-(1/3+1/4+......+1/17)
A<4/9-(1/3+1/4+.......+1/17)<1/2=4/8
Vậy a<1/2(đpcm)--------------------------Mình làm hơi dài nhé----------------------------------