1/2×4+1/4×6+1/6×8+1/8×10......+1/98×100
=1/4(1/1*2+1/2*3+1/3*4+...+1/49*50)
=1/4*[ (1-1/2) + (1/2-1/3) + (1/3-1/4) + ... + (1/49 - 1/50)]
=1/4*[ 1 - 1/50]
=49/200
1/2*4+1/4*6+1/6*8+1/8*10+...+1/98*100
=1/2(1/2-1/4)+1/2(1/4-1/6)+...+1/2(1/98-1/100)
=1/2(1/2-1/4+1/4-1/6+...+1/98-1/100)
=1/2(1/2-1/100)
=1/2*49/100
=49/200
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