Grade 12Algebra

Tr = ( 1 + 1/r^2 + 1/(r+1)^2 )^1/2 . Calculate sum of Tr where r varies from 1 to n.

Kinjal Shah

12 Years agoGrade 12

1 Answer

Arun Kumar

12 Years ago

$T_{r}=\sqrt{1+1/r^2+1/(r+1)^2} \\=>T_{r}=\sqrt{(r(r+1))^2+r^2+(r+1)^2}/(r(r+1)) \\=>T_{r}=(r(r+1)-r+(r+1))/(r(r+1)) \\=>T_{r}=1-(1/(r+1))+(1/r) \\=>\sum_{1}^{n}T_{r}=1+1-1/(n+1)=2-1/(n+1)$

Arun Kumar

IIT Delhi

Askiitians Faculty

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Tr = ( 1 + 1/r^2 + 1/(r+1)^2 )^1/2 . Calculate sum of Tr where r varies from 1 to n.

Kinjal Shah

1 Answer

Arun Kumar

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