estudier
f(n) = integer nearest sqrt(n)
1/f(1) + 1/f(2) + ...........+1/f(9999) +1/f(10000) = ?



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mahmit2012
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dw:1350239055071:dw

estudier
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That looks promising...

estudier
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So when is f(n) = m?

experimentX
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*

estudier
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Get rid of them nasty radicals as well.....

sara12345
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f(n) would range from 1 to 100

sara12345
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how to get rid of radical

estudier
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f(n) = a when (a1/2)^2 < n < (a+1/2)^2
(I'm using a)

sara12345
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ok

estudier
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Think I will leave this one up overnight in case people want to think more about it....

mukushla
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and im watching :)

sara12345
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does this involve integrals ?

estudier
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Certainly not! (I'm not that fond of calculus)

sara12345
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2a is the window for n until a increments

sara12345
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is this right direction

estudier
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Yes! Now u have the pattern, away u go....:)

sara12345
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so
f(n) = a
a = 1 ; 2.1 times
a = 2 ; 2.2 times
....
a = 99; 2.99 times
a = 100; 2.100/2 times

estudier
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Then the sum is ?

estudier
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The last bit is just some counting (don't overcount)

sara12345
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lol its easy

sara12345
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2a.1/a
a would cancel out !
99*2 + 1
= 199

estudier
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Yes, well done...

sara12345
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nice exercise thnk you :)

estudier
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yw

estudier
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Since it has been solved I will close it after all....