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Define the function pn(t)=(1)n(t)n.
1. Calculate p3(2).
2. Calculate p2(3).
3. Calculate p4(3).


Consider the following calculation of Δp2(t): since p2(t)=(1)2(t)2=(t)2, we may calculate Δp2(t)=((t+1))2(t)2=(t1)2(t)2=(t1)(t)(t)(t+1). We may express this as a multiple of (t)1 because Δp2(t)=(t1)(t)(t)(t+1)=[(t)][(t1)(t+1)]=(t)1(2)=2[(1)1(t)1]=2p1(t). 4. Calculate Δp3(t). Express your answer as a number multiplied to some pm(t).
5. Calculate Δp4(t). Express your answer as a number multiplied to some pm(t).
6. Do you notice a pattern developing for your answers to numbers 4 and 5? What is it?