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
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
Write out the sequence. You can see that U1=−1, U2=2, U3=−3, U4=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 Un=−Un−1±1 but you need to find a way to write the ±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).