1/10+1/40+1/88+1/154+1/238+1/340=
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![1/10+1/40+1/88+1/154+1/238+1/340=](/uploads/image/z/986605-61-5.jpg?t=1%2F10%2B1%2F40%2B1%2F88%2B1%2F154%2B1%2F238%2B1%2F340%3D)
1/10+1/40+1/88+1/154+1/238+1/340=
1/10+1/40+1/88+1/154+1/238+1/340=
1/10+1/40+1/88+1/154+1/238+1/340=
1/10+1/40+1/88+1/154+1/238+1/340
=1/3×(3/10+3/40+3/88+3/154+3/238+3/340)
=1/3×(1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17+1/17-1/20)
=1/3×(1/2-1/20)
=1/3×9/20
=3/20
1/10+1/40+1/88+1/154+1/238+1/340
=1/3(1/2-1/5+1/5-1/8+...+1/17-1/20)
=1/3*9/20
=3/20
10=2×5
40=5×8
88=8×11
154=11×14
238=14×17
340=17×20
∴可得:
3/10=(1/2)-(1/5)
3/40=(1/5)-(1/8)
3/88=(1/8)-(1/11)
...
3/340=(1/17)-(1/20)
累加,可得:
3S=(1/2)-(1/20)=9/20
S=3/20
1/10+1/40+1/88+1/154+1/238+1/340
=1/(2×5)+1/(5×8)+1/(8×11)+1/(11×14)+1/(14×17)+1/(17×20)
=1/3×(1/2-1/5)+1/3(1/5-1/8)+1/3(1/8-1/11)+1/3(1/11-1/14)+1/3(1/14-1/17)+1/3(1/17-1/20)
=1/3(1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17+1/17-1/20)
=1/3×(1/2-1/20)
=3/20