Suppose a1=2,an+1=12(an+2an). assuming an has a limit, find limn→∞an= . hint: let a=limn→∞. then, since an+1=12(an+2an), we have a=12(a+2a). now solve for a.

Looks like the sequence might be



Assume that . Then taking the limit of both sides, we have



But in order for the sequence to converge, only one of these values must be true. Since , each successive number will also be positive, so the limit must be .