SOLUTION: Hello this is a mathematical induction prove question I need help with. 1. Show that, for every positive integer n: 1 + 2 + 2^2 + 2^3 + … + 2^(n-1) = 2^n - 1

We show that it's true for n=1.



Then we find out what would happen if there were some positive integer k,
for which it were true.  If it were true for n = k, then we would have:



If that were true, we would be able to add 2k to both sides and
it would still be true.  Then we would have:









That is the original expression with k+1 substituted for n.

So if we could find a positive integer k so that the equation were true,
then we would know that it would have to also be true for the next higher
positive integer.

Now we DO have a positive integer k=1 so that the equation is true! That's
because at the first we showed that it is true when n=k=1, so that means it
is true for n=2.  Now, the fact that it's true for n=2 shows that it's also
true for n=3, and so on and on, through all the positive integers.

Edwin