Why is $\sum_{i=1}^6 2^i = 2^7-2$? 
Why is $$\sum_{i=1}^6 2^i = 2^7-2$$ 


$$\sum_{i=1}^6 2^i =2+2^2+2^3+2^4+2^5+2^6$$ $$= 2(1+2+2^2+..+2^5) = 2{2^6-1\over 2-1} =2^7-2$$
We have generaly $$1+x+x^2+...+x^n = {x^{n+1}-1\over x-1}$$
