Question 843411
That is a geometric series,
the sum of the first 17 terms of the form
{{{b[n]=2^(n-1)}}} ,
because {{{2^16=2^4*2^10=64*1024=65536}}} .
That sum is {{{SUM=1+2+2^2+2^3+"..."+2^16}}} and
{{{2*SUM=2+2^2+2^3+"..."+2^16+2^17}}} , so
{{{2*SUM-SUM=2^17-1}}}
{{{(2-1)*SUM=131072-1}}}
{{{SUM=highlight(131071)}}}
 
NOTE:
Your teacher/instructor may insist on seeing formulas, such as
{{{sum(b[0]*r^(n-1), 1,n)=b[0]*(r^n-1)/(r-1)}}} , or {{{SUM[n]=b[0]*(r^n-1)/(r-1)}}} .
Humoring teachers and bosses may be essential to survival,
but I do not believe math is about memorizing.
Remembering ideas that led others to a way to calculate results is OK.
That way we do not have to rediscover gunpowder every time,
but I refuse to memorize.