Calculate the sum 1 + 1/2 + 1/2^2 + 1/2^3 + 1/2^4 + 1/2^5

I have the highest regard for Giorgiana - she answered a
real tough question of mine  in an outstanding
way.

However, I disagree with this
answer.

I have both an algebraic way and a non-
algebraic way to do this.

Note that each sum
gets you half way between a starting point of first starting with 0 and
2

case in point 1 is 1/2 way between 0 and 2 and
you have 1 to go.

add 1/2 to 1 you are half way between 1
and 2 and only have 1/2 to go.

Sum = 2 - 1/2^5 =
1
31/32

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another
way:

consider sum*2 = 2 + 1 +1/2
+.....1/2^4

subtract sum     =      1 + 1/2
+..............1/2^5

2 - 1/2^5 what I just said
a different
way.

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clearly
the sum is greater than 1 since that is your first term and you add positive numbers to
it.