Math

Calculus Level 1

Find:

1 2 + 1 4 + 1 8 + 1 16 + 1 64 + 1 128 + 1 256 + 1 512 + … \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{64} + \frac{1}{128} + \frac{1}{256} + \frac{ 1 }{512} + \ldots

None of this 0 Infinity 1

Shankar Captain by Shankar Captain , 28, India

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4 solutions

Thales Castro
Jun 14, 2015

I had to consider that you forgot 1/32 by accident:

3 Helpful 0 Interesting 1 Brilliant 0 Confused
Peter Mattock
Jun 13, 2015

Technically incorrect as your original image misses the fraction 1/32, and so the sequence isn't geometric, but I guessed that was an error. Solved the same way you did.

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Noel Lo
Jun 7, 2015

1 2 + 1 4 + 1 8 + 1 16 + 1 32 + . . . . = 1 2 1 − 1 2 = 1 \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32}+.... = \frac{\frac{1}{2}}{1-\frac{1}{2}} = \boxed{1}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

The answer will get infinite close to 1, but it will never actually reach 1.

Mickey Huff - 6 years ago

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I put infinity thinking the same but how is 1 possible

Richard Feynman - 5 years, 10 months ago
Pankaj Bharti
Jun 16, 2015

(1-1/2) + (1/2-1/4) + ( 1/4-1/8) + ( 1/8-1/16) + ( 1/16-1/64) + ( 1/64-1/128) + _ _ _ =1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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