convergence of square of a geometric series Given
$ \sum_{j=0}^\infty [2.67(0.8^j) - 1.67(0.5^j)]  $ 
Does the above series converge because the terms are a sum of two convergent geometric series?
How can I prove the square is convergent as well?
$ \sum_{j=0}^\infty [2.67(0.8^j) - 1.67(0.5^j)]^2 < \infty  $
Do I expand the square, and say that the indexed terms in the three terms are still $ < 1 $ so the square also converges? 
Thanks

Since the series $$\sum_{j=0}^\infty2.67(0.8^j)$$
is absolutely convergent same applies to
$$\sum_{j=0}^\infty1.67(0.5^j)$$
So is their sum. Also since $$\sum_{j=0}^\infty1.67^2(0.25^j)$$
is absolutely convergent and
$$\sum_{j=0}^\infty(-2)\cdot2.67\cdot 1.67(0.4^j)$$
is also absolutely convergent. And for last
$$\sum_{j=0}^\infty2.67^2(0.64^j)$$
Is also absolutely convergent we have that their sum is also convergent which is $$\sum_{j=0}^\infty[2.67(0.8^j)+1.67(0.5^j)]^2$$
