Find the upper-bound for the summation, such that: (using the lowest possible integer)

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Find the upper-bound for the summation, such that: (using the lowest possible integer)

Mathematics
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it feels like there is something missing in the post
oops
\[\sum_{n=4200}^{x}n ^{1.5} \ge 1.0 \times 10^{8}\]

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not sure if possible. I could solve it if it was something like 5n
does this have anything to do with a remainder thrm?
I want to solve it for a game. Putting in random numbers, the closest integer I could get to have the same as close as possible to 100 million is 4563
*starting at 4220 >_>
Wolfram gives me weird zeta functions or harmonic numbers
10^8, or 10^7?
100 million, so 10^8 (if I did that right)
\[\int_{4200}^{x}x^{1.5}dx=x^{2.5}/2.5-(4200)^{2.5}/2.5\] \[x^{2.5}/2.5-(4200)^{2.5}/2.5=10^8\] \[x^{2.5}-(4200)^{2.5}=2.5*10^8\] \[x^{2.5}=(4200)^{2.5}+2.5*10^8\] \[x=((4200)^{2.5}+2.5*10^8\])^{1/}
ugh ... firefox crashed at the end of that
\[x=((4200)^{2.5}+2.5*10^8)^{1/2.5}=4545.ddd\]
I tried integrals, I must have done it wrong.
http://www.wolframalpha.com/input/?i=sum%28n%3D4200+to+4545%29n^%281.5%29
letting x=4545 seems to be fair
oh, I see what I did wrong. Thank you :D
yw

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