Solution
= Solution
Both sums are <geometric series>. For first term $a$ and common ratio $r$ with $|r|<1$, the sum is $a/(1-r)$. Taking the initial term to be $2$ gives
$$
\boxed{2+1+\frac12+\frac14+\cdots=\frac2{1-1/2}=4,}
$$
and
$$
\boxed{2-1+\frac12-\frac14+\cdots=\frac2{1+1/2}=\frac43.}
$$
Both have <absolute convergence> because the series of absolute values has ratio $1/2$.