You can put this solution on YOUR website! please help me with this mathematical induction 1/2^1+1/2^2+1/2^3+....+1/2^n =1-1/2^n.
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please help me by proving this statement using mathematical induction + ... + .
n=1: Ok for n=1. This is the base-case.
Assume it is true for n=k: that is, + ... + = holds for n=k. This is the hypothesis statement.
Now look at the case n=k+1:
+ ... +
If we exclude the very last term for a second, the remainder is the same case as n=k, which we can re-write by applying the hypothesis:
= +
Putting everthing over a common denominator (step-by-step):
=
=
=
Dividing the numerator by the denominator:
= DONE (the hypothesis leads to truth for n=k+1)
