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FP1

Question 10
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Can someone explain what its happening from f(k+1) why are they adding 2 to the power and from 2^2.. to 4[2^2k-1 + 3^2k-1]

Reply 1

nerak99

Well for some reason they want to have a power 2k-1 and hence they make 2k+1=2k-1+2 in the power. Allowing them to take the 2^2 out.
They spilt the 3^2 (=9) into 4 + 5 and so they can put the 3^(2k-1) with the factor of 4 and separate out the other 5.

Does that answer?

Reply 2

123PC

Original post by nerak99

Well for some reason they want to have a power 2k-1 and hence they make 2k+1=2k-1+2 in the power.

They are keeping 2k-1 in the power because that is divisible by 5 (since you've assumed it is true for n=k), which lets them substitute f(k) in the f(k+1) equation.