Please show all work:
Let P_{1} = 1
If x is odd then P_{x}_{+1} = 2P_{x}
If x is even then P_{x+1} = 2P_{x} +1
Prove that 2P_{x+1} + 2P_{x+1} +1 = P_{x+2} is true and then solve it.
First note that
But if the given relation were true then for x=1, we should have.
Rather by definition of P, it will satisfy . Let us prove this.
If x=2k, even, then
.
If x=2k-1, odd, then
.
Now to solve the relation.
Hence
Let P1 = 1 If x is odd then Px+1 = 2Px If x is even then Px+1 = 2Px +1 Show this is true and solve it: 2Px+1 + 2Px+1 +1 = Px+2
Please show all work: Let If x is odd then If x is even then Prove that is true and then solve it. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
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