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Grade 12Algebra

what is sum to n terms of (4/123)+(5/234)+(6/345)................................................(n+3)/n(n+1)(n+2)

judin varghese

12 Years agoGrade 12

1 Answer

Arun Kumar

12 Years ago

Doing little manipulation in the expression

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

Simplify to get the answer

Arun Kumar

IIT Delhi

Askiitians Faculty

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