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The sum of series (1)^(2)/(1.2!)+(1^(2...

The sum of series
`(1)^(2)/(1.2!)+(1^(2)+2^(2))/(2.3!)+(1^(2)+2^(2)+3^(2))//(3.4!)+..+(1^(2)+2^(2)+…+n^(2))/(n.(n+1))!+..infty` is equals to

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