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 Home > Just Math > Calculus Sooner or later, all math leads to Calculus, no matter how much we would like to beleive that isn't true. Here's our Calc section... Brush up on your college math, pull out a your dusty textbook and get comfy.
A student John starts with the familiar series 1 + 1/2 + 1/4 + 1/8 + . . . .

He then takes the average of each adjacent pair of terms and inserts it between the terms to obtain the new series 1 + 3/4 + 1/2 + 3/8 + 1/4 + . . . .

He divides this by two, because there are now twice as many terms as before. That gives

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

He repeats the process indefinitely. For example, the next pair of steps gives

1/2 + 7/16 + 3/8 + 5/16 + 1/4 + 7/32 + 3/16 + 5/32 + 1/8 + ...

then

1/4 + 7/32 + 3/16 + 5/32 + 1/8 + 7/64 + 3/32 + 5/64 + 1/16 + ...

What exact limit will the series approach?

 (Solution Posted, 4 Comments) Submitted on 2024-06-11 by K Sengupta
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