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Find-the-whole-part-of-A-A-1-2-1-3-1-4-1-9999-1-10000-




Question Number 21578 by ANTARES_VY last updated on 28/Sep/17
Find  the  whole  part  of  A?  A=(1/( (√2)))+(1/( (√3)))+(1/( (√4)))+......+(1/( (√(9999))))+(1/( (√(10000)))).
$$\boldsymbol{\mathrm{Find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{whole}}\:\:\boldsymbol{\mathrm{part}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{A}}? \\ $$$$\boldsymbol{\mathrm{A}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{4}}}+……+\frac{\mathrm{1}}{\:\sqrt{\mathrm{9999}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{10000}}}. \\ $$
Commented by Tinkutara last updated on 28/Sep/17
Almost similar to KVS JMO 2016.  Solutions are available on net.
$$\mathrm{Almost}\:\mathrm{similar}\:\mathrm{to}\:\mathrm{KVS}\:\mathrm{JMO}\:\mathrm{2016}. \\ $$$$\mathrm{Solutions}\:\mathrm{are}\:\mathrm{available}\:\mathrm{on}\:\mathrm{net}. \\ $$

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