Let
R1=1621+1621+1621+1621+1621+...R2=1621−1621−1621−1621−1621−...R3=1621+1621−1621+1621−1621+...R4=1621−1621+1621−1621+1621−....
Given that the values of the four infinitely nested radical expressions above can be expressed
R1=qp1,R2=qp2,R3=qp3,R4=qp4
where p1,p2,p3,p4,q are positive integers with gcd(pi,q)=1 for 1≤i≤4, find p1+p2+p3+p4.
Clarification: as a sequence, R4 is defined in the following way: R41:=1621,R4n:=1621−1621+R4n−1,
where R4n is n-th term of the sequence. R4:=n→∞limR4n.
R3 is defined analogously.
Warning: in R4 you may need to extract square root from a negative number. This root is always principal (i.e −2=i2, not −i2 ).
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