2+5+8+14+······+101的简便计算,该怎么算啊?
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2+5+8+14+······+101的简便计算,该怎么算啊?
![2+5+8+14+······+101的简便计算,该怎么算啊?](/uploads/image/z/16190592-24-2.jpg?t=2%2B5%2B8%2B14%2B%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%2B101%E7%9A%84%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97%2C%E8%AF%A5%E6%80%8E%E4%B9%88%E7%AE%97%E5%95%8A%3F)
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
= 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