[math-fun] Look and divide

Hello Math fun, read any fraction hereunder as: (quantity of digits used by the last term) ______________________________________________ (quantity of digits used in the sequence so far) Does the sum of all terms converge towards a precise number? (Sorry if this is old hat) Best, É. 0 1/1 2/3 2/5 2/7 2/9 2/11 3/14 3/17 3/20 3/23 3/26 3/29 ... (Example: the last fraction reads: "The preceding fraction uses 3 digits and the digits used so far in the sequence are 29")