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Thread: factorial revisited

  1. #1
    An Urch Guru Pundit Swami Sage
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    factorial revisited

    Find the value of 1.1! + 2.2! + 3.3! + ......+n.n!

    (1) n! +1
    (2) (n+1)!
    (3) (n+1)!-1
    (4) (n+1)!+1
    (5) None of these

  2. #2
    An Urch Guru Pundit Swami Sage cubicle's Avatar
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    by putting answr choices back in q

    3) what is Official Answer?
    rhymes with luck

    British-American-Tobacco's CEO: "Quitters never win,winners never quit"

  3. #3
    Within my grasp!
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    Answer is (n+1)!-1

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

    = (n+1)!-2+1 =(n+1)!-1

  4. #4
    Eager! 700plus2010's Avatar
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    ashk29

    Could you please explain the rules to your last step?
    I understand that (n+1)*n! = (n+1)! But I don't see how to get the "-2"

  5. #5
    Trying to make mom and pop proud
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    sum= 1.1! + 2.2! + 3.3! . . . . n.n!
    adding 1 both sides

    sum + 1 = 1 + 1.1! + 2.2! + 3.3! . . . . n.n!
    2! + 2.2! + 3.3! . . . . n.n!
    2! (1+2) + 3.3! . . . . n.n!
    3! + 3.3! . . . . n.n!
    3! (1+3) . . . . n.n!
    4! ... n.n!
    at the end you will get (n+1)!

    so sum= (n+1)! - 1

  6. #6
    Trying to make mom and pop proud
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    lets say n=3...the sum will be 1+2*2+3*3*2*1 = 1+4+18=23

    put n =3 in options....only c satisfies.....for all values of n. hence C

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