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    Can someone explain how to do this please?
    By writing down the first terms or otherwise, find the recurrence formula that defines the following sequences:
    Un = (-1)^n n
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    (Original post by Purpleunicorn197)
    Can someone explain how to do this please?
    By writing down the first terms or otherwise, find the recurrence formula that defines the following sequences:
    Un = (-1)^n n
    is that

    U_n = \left(-1\right)^n \times n ????
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    (Original post by dskinner)
    is that

    U_n = \left(-1\right)^n \times n ????
    yes
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    (Original post by Purpleunicorn197)
    yes
    Well finding the first term is easy, let n be any number.

    put in 1
    you get -1 out

    put 2
    you get -1 out

    put in 64378268427916547924789136579824 758931
    you still get -1 out

    but i don't quite understand the second part :/

    Zacken what would you do for the second bit?
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    (Original post by Purpleunicorn197)
    yes
    Write out the sequence. You can see that U_1 = -1, U_2 = 2, U_3 = -3, U_4 = 4, etc...

    i.e: to go from the first term to the second term, you need to multiply the result by -1 and then either add 1. To go from the second to the third, you need to multiply by -1 and then subtract 1.

    So you should be thinking U_n = -U_{n-1} \pm 1 but you need to find a way to write the \pm 1 such that it adds one when finding the second term (i.e: even cases) and subtracts one when finding odd terms. Think about it in terms of (-1)^{f(n)}.
 
 
 
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