Algebric sum

Algebra Level 3

S = 1 / 2 + 2 / 4 + 3 / 8 + 4 / 16 + . . . . . . . . 1/2+2/4+3/8+4/16+........

S = .....

THIS IS UNORIGINAL (AITMO 2013/9)


The answer is 2.

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1 solution

Math Man
Oct 6, 2014

S = 1 / 2 + 2 / 4 + 3 / 8 + 4 / 16 + . . . . . . . . S = 1/2+2/4+3/8+4/16+........ ----(1)

1 / 2 S = 1 / 4 + 2 / 8 + 3 / 16 + . . . . . 1/2 S = 1/4+2/8+3/16+..... ----(2)

(1)-(2)

1 / 2 S = 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + . . . . . . . . . 1/2 S = 1/2+1/4+1/8+1/16+.........

1 / 2 S = 1 / 2 ( 1 1 / 2 ) 1/2 S = \frac{1/2}{(1-1/2)} = 1

S = 2 S = \boxed{2}

my first "proper" solution

math man - 6 years, 8 months ago

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Lol what is unoriginal :p

Krishna Sharma - 6 years, 8 months ago

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i take it somewhere

math man - 6 years, 8 months ago

Great solution!

I was confused by your use of 1/2S . \textbf{ 1/2S} .

On my screen there is little space between the 2 and S suggesting the value, 1/(2S) . \textbf{1/(2S)}.

I would suggest using, 1 2 S or even better, S / 2. \frac{1}{2} S \text{ or even better, } S/2.

Michael Fischer - 6 years, 7 months ago

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