Question

1/5×8+1/8×11+1/11×14+……+1/98×101=

Answer 1

有括号吗？
（1）1/5×8+1/8×11+1/11×14+……+1/98×101
=8/5+11/8+14/11+......+101/98
=(1+3/5)+(1+3/8)+(1+3/11)+......+(1+3/98)
=1+3/5+1+3/8+1+3/11+......+1+3/98
=32+3/5+3/8+3/11+......+3/98
=32+3(1/5+1/8+1/11+......+1/98)
调和级数，没有公式。只能直接计算：
=32+3x1.10660588103047......
=32+35.31981764309141......
=67.31981764309141......
如果有括号的话：
（2）1/(5×8)+1/(8×11)+1/(11×14)+……+1/(98×101)
=[3/(5×8)+3/(8×11)+3/(11×14)+……+3/(98×101)]/3
=[(1/5-1/8)+(1/8-1/11)+(1/11-1/14)+……+(1/98-1/101)]/3
=(1/5-1/8+1/8-1/11+1/11-1/14+……+1/98-1/101)/3
=(1/5-1/101)/3
=(101/505-5/505)/3
=(96/505)/3
=32/505

Answer 2

可以利用裂项相消的方法来求和

追问

求详解！