Question

怎样计算下列各题~~

①1/2＋1/4＋1/6＋1/31＋1/62＋1/124＋1/248＋1/496
②1/42＋5/42＋11/42＋13/42＋17/42＋19/42＋23/42＋25/42＋29/42＋31/42＋37/42＋41/42

Answer 1

①
1+1/2+1/4+1/8+1/16=2-1/16=31/16

1/2＋1/4＋1/6=11/12
1/31＋1/62＋1/124＋1/248＋1/496
=1/31×(1+1/2+1/4+1/8+1/16)
=1/31×31/16=1/16

所以，1/2＋1/4＋1/6＋1/31＋1/62＋1/124＋1/248＋1/496=31/16+1/16=2

②
1 5 11 13 17 19 23 25 29 31 37 41
+41 37 31 29 25 23 19 17 13 11 5 1
=42 42 42 42 42 42 42 42 42 42 42 42

所以，1+5+11+13+17+19+23+25+29+31+37+41=42×12/2

所以，1/42＋5/42＋11/42＋13/42＋17/42＋19/42＋23/42＋25/42＋29/42＋31/42＋37/42＋41/42=42×12/2/42=6