?
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 + ...
Puzzling
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
alex
Sum of infinite terms
put in formula --->
S = 16