#### Answer

False

#### Work Step by Step

Need to check the formula.
$\sum_{ i=1}^ 2(-1) ^i 2^i=0$
Then,
$\sum_{ i=1}^ 2(-1) ^i 2^i=(-1)^1 \cdot 2^1+(-1)^2 \cdot 2^2=2$
But $2 \neq 0$
This implies that $\sum_{ i=1}^ 2(-1) ^i 2^i \neq 0$
Hence, the statement is false.