For positive integers n, the integer part of the nth term

The digits long after the decimal point are not going to matter here, since they only make a minuscule contribution to the sum, and we only need a rough estimate. If we work out the first seven terms, truncating each to one decimal place, we have:

1.2
2.4
3.6
4.8
5.1
6.1
7.1

When we round each term down here by ignoring all of the digits after the tenths digit, we are reducing the value of each term by less than 0.1, so if we add the seven terms above, the estimate we get will be less than (7)(0.1) = 0.7 below the true sum. And if we add the seven terms above, we get 30.3, so the real sum is somewhere between 30.3 and 31.0, and C is the answer.