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Question-113465




Question Number 113465 by Algoritm last updated on 13/Sep/20
Commented by Her_Majesty last updated on 13/Sep/20
use your brains  (√(2019))≈45  how could 45((1/(45+2019))+(1/(45+2019^2 ))+...)  be greater than 1???  if you start to try with  (√2)((1/(2+(√2)))+(1/(2^2 +(√2)))) and (√3)((1/(3+(√3)))+...+(1/(3^3 +(√3))))  and (√4)((1/(4+(√4)))+...+(1/(4^4 +(√4)))) you might see  that (√n)Σ_(j=1) ^n (1/(n^i +(√n))) can only be a rational  number when (√n) is a rational number.  also it can never be a(√n) with a∈N
$${use}\:{your}\:{brains} \\ $$$$\sqrt{\mathrm{2019}}\approx\mathrm{45} \\ $$$${how}\:{could}\:\mathrm{45}\left(\frac{\mathrm{1}}{\mathrm{45}+\mathrm{2019}}+\frac{\mathrm{1}}{\mathrm{45}+\mathrm{2019}^{\mathrm{2}} }+…\right) \\ $$$${be}\:{greater}\:{than}\:\mathrm{1}??? \\ $$$${if}\:{you}\:{start}\:{to}\:{try}\:{with} \\ $$$$\sqrt{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2}+\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} +\sqrt{\mathrm{2}}}\right)\:{and}\:\sqrt{\mathrm{3}}\left(\frac{\mathrm{1}}{\mathrm{3}+\sqrt{\mathrm{3}}}+…+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} +\sqrt{\mathrm{3}}}\right) \\ $$$${and}\:\sqrt{\mathrm{4}}\left(\frac{\mathrm{1}}{\mathrm{4}+\sqrt{\mathrm{4}}}+…+\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{4}} +\sqrt{\mathrm{4}}}\right)\:{you}\:{might}\:{see} \\ $$$${that}\:\sqrt{{n}}\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{n}^{{i}} +\sqrt{{n}}}\:{can}\:{only}\:{be}\:{a}\:{rational} \\ $$$${number}\:{when}\:\sqrt{{n}}\:{is}\:{a}\:{rational}\:{number}. \\ $$$${also}\:{it}\:{can}\:{never}\:{be}\:{a}\sqrt{{n}}\:{with}\:{a}\in\mathbb{N} \\ $$
Commented by Algoritm last updated on 13/Sep/20
no correct
$$\mathrm{no}\:\mathrm{correct} \\ $$
Commented by Her_Majesty last updated on 13/Sep/20
then tell me what′s correct
$${then}\:{tell}\:{me}\:{what}'{s}\:{correct} \\ $$
Commented by mr W last updated on 13/Sep/20
Σ<2019×((√(2019))/(2019+(√(2019))))=((2019)/(1+(√(2019))))≈44  ⇒all answers are wrong!
$$\Sigma<\mathrm{2019}×\frac{\sqrt{\mathrm{2019}}}{\mathrm{2019}+\sqrt{\mathrm{2019}}}=\frac{\mathrm{2019}}{\mathrm{1}+\sqrt{\mathrm{2019}}}\approx\mathrm{44} \\ $$$$\Rightarrow{all}\:{answers}\:{are}\:{wrong}! \\ $$
Commented by mr W last updated on 13/Sep/20
exact value for Σ not possible!
$${exact}\:{value}\:{for}\:\Sigma\:{not}\:{possible}! \\ $$
Commented by Algoritm last updated on 13/Sep/20
answer  ?
$$\mathrm{answer}\:\:? \\ $$
Commented by mr W last updated on 13/Sep/20
the answer is that the question is  wrong! if you have a better answer,  then tell us!
$${the}\:{answer}\:{is}\:{that}\:{the}\:{question}\:{is} \\ $$$${wrong}!\:{if}\:{you}\:{have}\:{a}\:{better}\:{answer}, \\ $$$${then}\:{tell}\:{us}! \\ $$

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