Sum

Algebra Level 1

2^0+2^-1 + 2^-2 +..........


The answer is 2.

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2 solutions

use infinite of deret geometry

S~ = a /(1-r)

from equation , a=1 and r=1/2, substitution at S~

S~ = 1/(1-(1/2)) 1/(1/2) = 2

2 0 + 2 1 + 2 2 + . . . = 1 + 1 2 1 + 1 2 2 + . . . = 1 + 1 2 + 1 4 + . . . = 2 2^{0} + 2^{-1}+ 2^{-2}+... = 1+ \frac{1}{2^{1}} + \frac{1}{2^{2}}+... = 1 + \frac{1}{2}+ \frac{1}{4}+... = 2

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