Puzzles/Analytical Puzzles/Surprising Limit/Solution

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Puzzles|Analytical puzzles|Surprising Limit|Solution

  • Expand the argument of

Since sine is a periodic function, adding or subtracting multiples of can not change the result, thus the first few terms on the right hand side can be dropped (those first few where is a whole number thus n is greater or equal to z), and one is left with

Since for small (Taylor expansion of sine), the limit is

.