You know 1/7 = 0.14258. Can you predict what the decimal expansions of 2/7, 3/7, 4/7, 5/7, 6/7 are, without actually doing the long division? If so, how?
TÖRTEK (BEVEZETŐ) - 2. FELADATLAP
What is the sum of the first 20 terms of the series 1/5×6+1/6×7+1/7×8…? - Quora