Question

4/5➕2/15➕2/45➕2/135➕2/405➕2/1215怎么计算？

这题怎么解答

Answer 1

解:原式=12/15+2/15+2/45+2/135+2/405
+2/1215
=14/15+2/45+2/135+2/405+2/1215
=42/45+2/45+2/135+2/405+2/1215
=44/45+2/135+2/405+2/1215
=132/135+2/135+2/405+2/1215
=134/135+2/405/2/1215
=402/405+2/405+2/1215
=404/405+2/1215
=1212/1215+2/1215
=1214/1215
或者设原式=s，则
s=4/5+2/15+2/45+2/135+2/405+2/1215……①
3s=12/5+2/5+2/15+2/45+2/135+2/405……②
②一①得:2s=12/5+2/5-4/5-2/1215
s=6/5+1/5-2/5-1/1215
=7/5-2/5-1/1215
=1-1/1215
=1214/1215

Answer 2

4/5+2/15+2/45+2/135+2/405+2/1215
=1-1/5+2/15+2/45+2/135+2/405+2/1215
=1-3/15+2/15+2/45+2/135+2/405+2/1215
=1-1/15+2/45+2/135+2/405+2/1215
=1-3/45+2/45+2/135+2/405+2/1215
=1-1/45+2/135+2/405+2/1215
=1-3/135+2/135+2/405+2/1215
=1-1/135+2/405+2/1215
……
=1-1/1215
=1214/1215

Answer 3

4/5+2/15+2/45+2/135+2/405+2/1215
=12/15+2/15+2/45+2/135+2/405+2/1215
=14/15+2/45+2/135+2/405+2/1215
=42/45+2/45+2/135+2/405+2/1215
=44/45+2/135+2/405+2/1215
=132/135+2/135+2/405+2/1215
=134/135+2/405+2/1215
=402/405+2/405+2/1215
=404/405+2/1215
=1212/1215+2/1215
=1214/1215

Answer 4

设S=4/5+2/15+2/45+2/135+2/405+2/1215①
①×1/3得:4/15+2/45+2/135+2/405+2/3645②
①-②得:2S/3=4/5-2/15-2/3645=2/3-2/3645=（2*1215-2）/3645=2428/3645
S=(2428/3645)×（3/2）=3642/3645=1214/1215