Re: a series
what is the property of the following sum
\sum_{k=1}^{m}\frac{\cos{t\ln k}}{\sqrt k} as t
tends to \infty
where m=the lagerst integer witch is less than or
equal to \ln{\sqrt
\frac{t}{2\pi}}
Some calculations from Maple:
t ---- sum
100 ---- 1.12
1000 ---- 0.508
10^4 ---- -0.023 (negative)
10^5 ---- 3.483
10^6 ---- 1.669
10^7 ---- 8.954
10^8 ---- 0.854
10^9 ---- -0.544 (negative)
It appears highly oscillatory.
.
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