Thread: more of an algebra problem...

In the identity,

prove that

Thanks in advance

using mi is the way to go.

for n=0, lhs = rhs = 1/x
assume it holds for n
prove it still holds for n+1, using this hint 1/[(x+k)(x+n+1)] = [ 1/(x+k) - 1/(x+n+1) ] / (n+1)

What does it mean to prove something "in the identity"? Do you mean to prove that the first identity implies the second one? That would be surprising because I would expect one can choose is many ways to satisfy the first formula.

Originally Posted by emakarov

What does it mean to prove something "in the identity"? Do you mean to prove that the first identity implies the second one? That would be surprising because I would expect one can choose is many ways to satisfy the first formula.

I think the questions says if the first information is given ,we have to prove the second statement.
btw, the first one is is not an identity, and may be the words:"in the identity" are wrong.Its a "if...,then prove" type of problem.

Originally Posted by earthboy

In the identity,

prove that

Thanks in advance

My way is to,
from ,
put to get

Is this ok?
can you guys post other solutions..

Ah, so the first equality is true for all x.

Originally Posted by earthboy

My way is to,
from ,
put to get

This makes sense.