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What is the reason behind calculating GCD in Pollard rho integer factorisation?

algorithm,math,greatest-common-divisor,number-theory,clrs
This is the pseudo code for calculating integer factorisation took from CLRS. But what is the point in calculating GCD involved in Line 8 and the need for doubling k when i == k in Line 13.? Help please....

sum of series AP GP clrs appendix A.1-4

algorithm,math,infinite,clrs,gp
I am trying to prove an equation given in the CLRS exercise book. The equation is: Sigma k=0 to k=infinity (k-1)/2^k = 0 I solved the LHS but my answer is 1 whereas the RHS should be 0 Following is my solution: Let's say S = k/2^k = 1/2 +...