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lim( sin^n 1+cos^n 1)^n n tends to infinite ......................................................................
The jumps from n to n+1 are of size 1 and the size of a quadrant is π/2>1 so there are infinitely many integers n such that n mod 2π is in each of the four quadrants.For every n in the first quadrant (0,π/2) mod 2π, one knows that 01 and 1/sinn>1 hence xn>2.For every n in the third quadrant (π,3π/2) mod 2π, one knows that −1This proves that (xn) diverges.
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