Answer to Question #275675 in Algebra for Zahir

Question

8∑(j=1)2^j

Answer 1

Let us find the sum $\sum\limits_{j=1}^82^j$ using the formula for the sum of geometric progression $S_n=a_1\frac{q^n-1}{q-1}.$

In our case, $a_1=2,\ q=2,\ n=8.$

It follows that

$\sum\limits_{j=1}^82^j=S_8=2\frac{2^8-1}{2-1}=2\cdot 255=510.$