2+5+8+14+······+101的简便计算,该怎么算啊?_数学解答

2+5+8+14+······+101的简便计算,该怎么算啊?

人气：391 ℃　时间：2020-04-02 13:00:20

解答

2 + 5 + 8 + 14 + …… + 101
= 2 + 5 + ( 2 + 5 + 1 ) + ( 5 + 8 + 1 ) + …… + 101
= 2 + 5 + 8 + 14 + ( 8 + 14 + 1 ) + ( 14 + 23 + 1 ) + ( 23 + 38 + 1 ) + ( 38 + 62 + 1 )
= 2 + 5 + 8 + 14 + 23 + 38 + 62 + 101
= 8 + 3 + 6 + 12 + 21 + 36 + 60 + 99 + 8
= 99 + ( 60 + 36 + 3 ) + ( 21 + 12 + 6 ) + 16
= 99 + 99 + 39 + 16
= 240 + 13
= 253