Thing is, if I'm not mistaken, that series diverges.
Hey,
How is does it diverge? the expression p+qp−q<1 but p+qp−q→1 as p→∞ and q is small.
But considering only if they are real, positive, the "ratio" of this series is less than 1, so should converge? If I'm wrong, why would it diverge? Would love to know
Edit: I don't really mean ratio, but I mean each term is essentially getting smaller and should tend to zero.
How is does it diverge? the expression p+qp−q<1 but p+qp−q→1 as p→∞ and q is small.
But considering only if they are real, positive, the "ratio" of this series is less than 1, so should converge? If I'm wrong, why would it diverge? Would love to know
Edit: I don't really mean ratio, but I mean each term is essentially getting smaller and should tend to zero.
All because the terms tend to 0 doesn't mean the sum converges.
How is does it diverge? the expression p+qp−q<1 but p+qp−q→1 as p→∞ and q is small.
But considering only if they are real, positive, the "ratio" of this series is less than 1, so should converge? If I'm wrong, why would it diverge? Would love to know
Edit: I don't really mean ratio, but I mean each term is essentially getting smaller and should tend to zero.
The series is effectively 1+31+51+71+⋯ which diverges. The rest of the stuff inside the summation is independent of r (so you can take it out as a constant).
Not sure why you're considering p→∞, are we not looking at the same series?
The series is effectively 1+31+51+71+⋯ which diverges. The rest of the stuff inside the summation is independent of r (so you can take it out as a constant).
Not sure why you're considering p→∞, are we not looking at the same series?
Hey,
I understand what you mean, the series he gives would indeed diverge as the you could take out the two constants 2 and the expression above, leaving just 2r−11 and hence giving the series you described, but, I'm more worried about this: r=1∑∞2r−12(p+qp−q)4r−2=ln(2p+q)−2lnp+lnq Then went onto say that the the power gets removed.
If the power was removed, I understand your point, I also recognise this series as a divergent one. But why was the power removed?
I tried seeing a pattern when squaring this constant, but nothing came about.
I understand what you mean, the series he gives would indeed diverge as the you could take out the two constants 2 and the expression above, leaving just 2r−11 and hence giving the series you described, but, I'm more worried about this: r=1∑∞2r−12(p+qp−q)4r−2=ln(2p+q)−2lnp+lnq Then went onto say that the the power gets removed.
If the power was removed, I understand your point, I also recognise this series as a divergent one. But why was the power removed?
I tried seeing a pattern when squaring this constant, but nothing came about.
Ah TeeEm has mentioned that the text has a typo. That explains.