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If t(r)=(1^(2)+2^(2)+3^(2)+….+r^(2))/(1^...

If `t_(r)=(1^(2)+2^(2)+3^(2)+….+r^(2))/(1^(3)+2^(3)+3^(3)+…+r^(3)), S_(n)=sum_(r=1)^(n)(-1)^(r)t_(r)`, then `lim_(nrarroo)((1)/(3-S_(n)))=`

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The correct Answer is:
3/11
`S_(n)=(2)/(3) sum_(r=1)^(n)(-1)^(r)((1)/(r)+(1)/(r+1))`
`S_(n=(2)/(3)sum_(r=1)^(oo)((1)/(r)+(1)/(r+1))`
`S_(n)=(2)/(3)sum_(r=1)^(oo)`(((-1)^(r))/(r)-((-1)^(r+1))/(r+1))" "rArr" "(2)/(3)((-1)/(1)-0)=-2//3`
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