3|4+3|28+3|70+3|130+3|208=找规律计算

3|4+3|28+3|70+3|130+3|208=找规律计算
3|4+3|28+3|70+3|130+3|208=找规律计算

3|4+3|28+3|70+3|130+3|208=找规律计算
=3/（1*4）+3/(4*7)+3/（7*10）+.3/(13*16)
=3(1/(1*4)+1/(4*7)+.1/(13*16))
=1-1/4+1/4-1/7+.+1/13-1/16
=1-1/16
=15/16

用裂项法
原式=3(1/(1*4)+1/(4*7)+......1/(13*16))
=1-1/4+1/4-1/7+......+1/13-1/16
=15/16

15/16
3/4=1/1-1/4
3/28=3/(4*7)=1/4-1/7
3/70=1/10-1/13
3/130=1/10-1/13
3/208=1/13-1/16
所以相加，中间的项都抵消了，原式=1-1/16=15/16
或
3/4+3/28+3/70+3/130+3/208
=(1-1/4)+(1/4-1/7)+...

全部展开

15/16
3/4=1/1-1/4
3/28=3/(4*7)=1/4-1/7
3/70=1/10-1/13
3/130=1/10-1/13
3/208=1/13-1/16
所以相加，中间的项都抵消了，原式=1-1/16=15/16
或
3/4+3/28+3/70+3/130+3/208
=(1-1/4)+(1/4-1/7)+(1/7-1/10)+(1/10-1/13)+(1/13-1/16)
=1-1/16
=15/16
就是这样了。祝你学习进步！！！

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