Question

Can someone explain this, please?

Answer 1

If you notice the terms, they're

7, -21, 63, -189 and so forth.

7*-3 = -21  and -21 * -3 is 63 and so forth, meaning the "common ratio" is -3.

now, for a common ratio say "r", which is a fraction, namely less than ±1 and more than 0, or |r| < 1 ,  you do have a convergent sequence.

however this one notice, |-3| is 3, and that's greater than 1 clearly, therefore is divergent, meaning the summation has no finite value.