Let x be the sum of the values of sin(n) for the whole numbers 0 though n. (In radians, of course.)
Find the maximum A and minimum B such that
A < x < B
Adapted from AMS Page A Day Calendar by Evelyn Lamb December 7.
In a computer simulation the smallest and largest values I found (n = 100,000,000):
a: -0.1276709606109031
b: +1.9581586823233645
The sum from 1 to n should be strongly influenced by the boundary starting conditions: the first 3 terms are all positive. Not until the 4th term is there an angle greater than 180 degrees with a negative contribution. So it is not surprising that the min and max are skewed toward a positive value.
Interestingly, the average value for this a and b is: 0.9152438608562308,
which is fairly close to sinsum(1) = 0.8414709848078965
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Posted by Larry
on 2020-12-11 08:47:10 |
solution
