Question Number 114625 by bobhans last updated on 20/Sep/20

Answered by john santu last updated on 20/Sep/20

⇔k^4 +2k^2 +9=k^4 +6k^2 +9−4k^2                               = (k^2 −2k+3)(k^2 +2k+3)  S=Σ_(k=1) ^∞  (k/((k^2 −2k+3)(k^2 +2k+3)))  S=Σ_(k=1) ^∞ (1/4)((1/(k^2 −2k+3)) − (1/(k^2 +2k+3)))  S= (1/4)Σ_(k=1) ^∞ ((1/(k(k−2)+3)) − (1/(k(k+2)+3)))  S=(1/4)((1/2)+(1/3)−0)=(5/(24)).

Commented bybobhans last updated on 20/Sep/20

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