How to calculate the sum :
1/sqrt(10000) + 1/sqrt(10001) + 1/sqrt(10002) ... + 1/sqrt(1000000)

Question

How to calculate the sum :
1/sqrt(10000) + 1/sqrt(10001) + 1/sqrt(10002) ... + 1/sqrt(1000000)

turingtest · Answer

$$\Large\sum_{i=10^4}^{10^6}\frac1{\sqrt i}$$???

raden · Answer

yea, like that...

anonymous · Answer

maybe they mean to find floor of this !!

raden · Answer

but no said to find floor of this question..

anonymous · Answer

raden · Answer

hmmm... but i want to know using algebraic to solve it
give me idea mukushla

anonymous · Answer

anonymous · Answer

integral part means floor

raden · Answer

ohhh... i just know that "integral part means floor"
but i dont look its integral process??

anonymous · Answer

actually $${1\over\sqrt{k+1} + \sqrt{k}} < {1\over 2\sqrt{k}} < {1\over\sqrt{k-1} + \sqrt{k}}$$

anonymous · Answer

rationalize the denum for LHS and RHS of inequality u have$$\sqrt{k+1} - \sqrt{k} < {1\over 2\sqrt{k}} <\sqrt{k} - \sqrt{k-1}$$

anonymous · Answer

apply the sigma

raden · Answer

Ok i got it...
i think this problem can be solved with integral or simplify one by one that fractions lol... thanks mukushla

anonymous · Answer

very welcome