Wouter> nice! prod( k=1..m, A026147(k) ) / prod( k=1..m, A181155(k) ) approaches sqrt( 2 ) as m-> infinity goes like 1, 1/2, 2/3, 7/10, 286/405, 144305/204102, 276620298878/391202754597, ... (* those who abhor Mathematice lines, please look away : *) k=1/2;NestList[#/(#/. i->i+(k=2k))&,x[i],6] %/. x[i_]->i %/. i->1 %//N <Wouter. -----Original Message----- From: David Wilson Sent: Saturday, July 05, 2014 5:34 PM To: math-fun Subject: [math-fun] Problem I never solved I know the answer to this, but not how to derive it: What is the value of (((1/2)/(3/4))/((5/6)/(7/8)))/... <DW More to abhor: NestList[{#,#+Max[#]}&,1,6]/.List->Divide Divide::argrx: Divide called with 7 arguments; 2 arguments are expected. >> Divide[1, 1/2, 2/3, 7/10, 286/405, 144305/204102, 276620298878/391202754597] (-: rwg