S=Σ_(k=0) ^∞ ((3k^2 )/(2k^3 +2)) =? =Σ_(k=0) ^∞ (1/2)(((3k^2 )/(k^3 +1)))=Σ_(k=0) ^∞ (1/2)[(1/(k+1))+((2k−1)/(k^2 −k+1))] I dont know how to continue...Please Help.


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Question Number 136408 by nimnim last updated on 21/Mar/21

$S = \underset{k = 0}{\sum^{\infty}} \frac{3 k^{2}}{2 k^{3} + 2} = ?$ $= \underset{k = 0}{\sum^{\infty}} \frac{1}{2} (\frac{3 k^{2}}{k^{3} + 1}) = \underset{k = 0}{\sum^{\infty}} \frac{1}{2} [\frac{1}{k + 1} + \frac{2 k - 1}{k^{2} - k + 1}]$ $I d o n t k n o w h o w t o c o n t i n u e . . . P l e a s e H e l p .$
	Answered by Dwaipayan Shikari last updated on 21/Mar/21

	$\underset{k = 0}{\sum^{\infty}} \frac{1}{k + 1} \to D i v e r g e s (W h o l e s e r i e s d i v e r g e s)$
	Commented by nimnim last updated on 21/Mar/21

	$T h a n k y o u s i r . .$
	Answered by mathmax by abdo last updated on 21/Mar/21

	$without calculus the serie is divergent . . .!$
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