Anonymous
Anonymous asked in Science & MathematicsEngineering · 7 years ago

Find the formula for 1 + summation from j = 1 to n of j!*j.?

Find the formula for 1 + summation from j = 1 to n of j!*j. Wolfram alpha says it's (n+1)! but can someone explain how? Thanks in advance i'm really stuck.

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  • 7 years ago
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    ∑ = 1+[1+2.2! + 3.3! + 4.4! + 5.5! +... + n.n! ]

    Now you may need to think a little on this one but fact is: n.(n!) = (n+1).(n!) – n! so the series becomes:

    1+[2.1! + 3.2! + 4.3! + 5.4! +...+(n+1)n! - 1 - 2! - 3! - ... - n!]

    = 1+2!+3!+4!+5!+ .. +n!+(n+!)! - (1+2!+3!+4!+...+n!)

    Only one term does not cancel out, leaving:

    (n+1)! as the summation.

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