Algebra

$\frac{1}{1 \times 4} + \frac{1}{4 \times 7} + \frac{1}{7 \times 10}$ is basically:

1/3(1 - 1/4 + 1/4 -1/7 +1/7 - 1/10)

which is 1/3 $\times$ 9/10 = 3/10