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=1/4+1/3*（1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16)
=1/4+1/3*(1/4-1/16)
=1/4+1/16
=5/16

1/4+1/28=8/28=4/14
4/14+1/70=21/70=3/10
3/10+1/130=40/130=4/13
4/13+1/208=64/208+1/208=65/208=5/16
一要想一次性搞定,一个一个的加

1/4+1/28+1/70+1/130+1/208
28=4*7 70=7*10 130=10*13 208=13*16
1/4=1/3*(1-1/4) 1/28=1/3*(1/4-1/7) 1/70=1/3*(1/7-1/10)
1/130=1/3*(1/10-1*/13) 1/208=1/3*(1/13-1/16)
相加可得：1/4+1/28+1/70+1/130+1/208=1/3*{(1-1/4)+（1/4-1/7)+（1/7-1/10)+(1/10-1*/13)+(1/13-1/16)}=1/3*（1-1/16）=5/16

原式=1/(1*4)+1/(4*7)+1/(7*10)+1/(10*13)+1/(13*16)
=(1/3)(1-1/4+1/4-1/7+1/7....-1/16)
=5/16
不懂再问

1/4 = 1/3(1-1/4)

1/28 = 1/3(1/4-1/7)

1/70 = 1/3(1/7-1/10)

1/130 = 1/3(1/10-1/13)

1/208 = 1/3(1/13-1/16)

相加后1/3在括号外，里面可以消掉中间项保留（1－1/16）

1/3*15/16＝5/16

1/4+1/28+1/70+1/130+1/208
=8/28+1/70+1/130+1/208
=20/70+1/70+1/130+1/208
=21/70+1/1