利用数列极限的定义证明:lim(n→∞）3n+1/4n-1 = 3/4

考虑：
|(3n+1)/(4n-1) - 3/4|
=|4(3n+1)-3(4n-1) / 4(4n-1) |
=|(12n+4-12n+3) / 4(4n-1) |
=|7 / 4(4n-1) |
=(7/4) * |1/(4n-1)|
1,即有：3n1/(4n-1)
那么有：
|(3n+1)/(4n-1) - 3/4|
0,存在N=max{1,1/ε}
当n>N,都有|(3n+1)/(4n-1) - 3/4|