1/1*4+1/4*8+1/8*12+...+1/96*100=?

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1/1*4+1/4*8+1/8*12+...+1/96*100=?
1/1*4+1/4*8+1/8*12+...+1/96*100=?

1/1*4+1/4*8+1/8*12+...+1/96*100=?
1/4*8=(1/4-1/8)/4
1/8*12=(1/8-1/12)/4
1/12*16=(1/12-1/16)/4
.
1/96*100=(1/96-1/100)/4
所以原式=1/4+1/4(1/4-1/8+1/8-1/12+.-1/96+1/96-1/100)
=1/4+1/4*(1/4-1/100)
=31/100
您验算下,没算错的话,

1/(1×4)+1/(4×8)+1/(8×12)+...+1/(96×100)
=1/4+(1/4)(1/4-1/8+1/8-1/12+...+1/96-1/100)
=1/4+(1/4)(1/4-1/100)
=1/4+1/16-1/400
=124/400
=31/100

1/1*4+1/4*8+1/8*12+...+1/96*100
=1/4*(1-1/4+1/4-1/8+1/8-1/12+...+1/96-1/100)
=1/4*(1-1/100)
=99/400