Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
evaluate the infinite series 8+4+2+1+... what does this mean??
3 Answers
- Φ² = Φ+1Lv 75 years ago
It is asking for the limit of the sum of this infinite series.
1 = ½ + ¼ + ⅛ + ⅟₁₆ + ⅟₃₂ + ⅟₆₄ + ...
Multiplying through by 16 to get 8 as the first term
16 = 8 + 4 + 2 + 1 + ½ + ¼ + ⅛ + ...
- PuzzlingLv 75 years ago
That's a geometric sequence:
8, 4, 2, 1, 1/2, 1/4, 1/8, etc.
The first term is 8.
The common ratio is 1/2 (because each term is 1/2 the prior term).
The formula for the sum of an infinite geometric sequence (where |r|<1) is:
S = a(1/(1 - r))
a : first term (8)
r : common ratio (1/2)
S = 8(1/(1 - 1/2))
S = 8(1/(1/2))
S = 8(1 * 2)
S = 8*2
S = 16
Answer:
8 + 4 + 2 + 1 + 1/2 + 1/4 + 1/8 + ... = 16
