Explain why the two facts from part a) imply that 1 + 2 + 2 2 + 2 3 + 2 4 + 2 5 + 2 6 = 2 7 − 1 {\displaystyle 1+2+2^{2}+2^{3}+2^{4}+2^{5}+2^{6}=2^{7}-1} .
