a) có 231=2.230=2.810
321=3.320=3.910
vì 2.810 < 3.910 nên 231 < 321
b)
có S = 1 + 2 + ... + 250
<=> S = 20 + 21 + 22 + 23 + ... + 250
=> 2S = 2(20 + 21 + 22 + 23 + ... + 250) = 21 + 22 + 23 + ... + 251
=> 2S - S = 21 + 22 + 23 + ... + 251 - ( 20 + 21 + 22 + 23 + ... + 250)
=> S = 21 + 22 + 23 + ... + 251 - 20 - 21 - 22 - 23 - ... - 250
=> S = 251 - 20
=> S = 251 -1 < 251
=> S < 251
\(2^{31}=2^{30}.2=\left(2^3\right)^{10}=8^{10}\)
\(3^{31}=3^{30}.3=\left(3^3\right)^{10}.3=9^{10}.3\)