1/8+1/24+1/48+...+1/2400
=1/4(1/2+1/2*3+1/3*4+...+1/24*25)
=1/4(1-1/2+1/2-1/3+1/3-1/4+...+1/24-1/25)
=1/4(1-1/25)
=(1/4)(24/25)
=6/25
1/(2*4)+1/(4*6)+1/(6*8)+……+1/(48*50)
=[(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+……+（1/48-1/50)]/2
=(1/2-1/50)/2
=6/25
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