Recursion relation for C-G coefficients

[Alien]

From J.J. Zakurai page no.222-225:

We know that Clebsch-Gordan coefficients vanish unless m=m1+m2. Then,

(1) why is that the terms in recursion relation doesn't vanish? since m1+m2=m+1 or m1+m2=m-1 in eqn.(3.7.49).

(2) why is again in the example shown in eqn.(3.7.54), m1+m2=m?

I couldn't understand the whole thing. Somebody please help.

 

[Alien]

Excuse me, the book is- "Modern Quantum Mechanics" by J.J. Sakurai

 

[malawi_glenn]

what edition?

 

[Alien]

It is the 'revised edition' printed in 2005.