mathematical treasure part1

k
i know laatex is in trouble
the ques is
A =1/√2+1√3+1/√4.....................1/√10000

find [A]

where[x] represents GINT

its the time 4 the answer

\frac{1}{\sqrt{m}}=\frac{2}{\sqrt{m}+\sqrt{m}}<\frac{2}{\sqrt{m}+\sqrt{m-1}}

on rationalizing

2(\sqrt{m}-\sqrt{m-1})

so we get

\frac{1}{\sqrt{2}}<2(\sqrt{2}-{\sqrt{1}})

\frac{1}{\sqrt{3}}<2(\sqrt{3}-{\sqrt{2}})

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\frac{1}{\sqrt{10000}}<2(\sqrt{10000}-\sqrt{9999})

alternate terms r cutting so we r left with

A<2(100-1)=198

now again

\frac{1}{\sqrt{m}}=\frac{2}{\sqrt{m}+\sqrt{m}}>\frac{2}{\sqrt{m}+{\sqrt{m+1}}}

==2(\sqrt{m+1}-\sqrt{m})

A>2(\sqrt{10001}-\sqrt{2})>197

So we get

197<A<198

so [A]=197

hey mani how was aieee?

check ur chatbox

HeY TrY ThIs AgAiN

gud one and nice approach

rohan already solved one this kind b4

let me find ...

Is the ques

A =1/√2+1√3+1/√4.....................1/√10000

or
A =1/√2+1/√3+1/√4.....................1/√10000

Add question otherwise there is no sense in asking to answer

even me i cant see the ques

meko q ni dikh ra

this one`s a pretty good one. let others try

is there a way to *solve* this?

this 1 is damn cool
have a try on it [1]