1/2*4+1/4*6+1/6*8+.+1/98*100怎样解?急

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1/2*4+1/4*6+1/6*8+.+1/98*100怎样解?急
1/2*4+1/4*6+1/6*8+.+1/98*100怎样解?
急

1/2*4+1/4*6+1/6*8+.+1/98*100怎样解?急
因为1/n(n+2)=[1/n-1/(n+2)]/2
所以
1/2*4+1/4*6+1/6*8+.+1/98*100
=1/2*(1/2-1/4)+1/2*(1/4-1/6)+1/2*(1/6-1/8)+...+1/2*(1/98-1/100)
=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+...+1/98-1/100)
=1/2*(1/2-1/100)
=49/200.

1/2*4+1/4*6+1/6*8+......+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+......+1/98*100怎样解？
=1/2(1/2-1/4+1/4-1/6+1/6-1/8+… …+1/98-1/100)
=1/2(1/2-1/100)
=1/2*49/100
=49/200

1/n×（n+1）=（n+1-n）/n×（n+1）=1/n-1/(n+1)
原式=1/2*(1/1*2+...+1/49*50)=1/2*(1-1/50)=49/100

|1/4-1/2|+|1/6-1/4|+|1/8-1/6|+```+|1/2008-1/2006| 1/2+1/4+1/6+1/8+.1/n 1+6+6+8+4+2+6+6+5+4+4+1+4+7+45 1+1/2+4+1/2+4+6+1/2+4+6+8+.+1/2+4+6+8...+20 1/2*4+1/4*6+1/6*8+1/8*10+---+1/198*200 10,1,8,1,6,2,4,6,2,（）. 1/2*4*6+1/4*6*8+1/6*8*10+.+96*98*100 1/2*4+1/4*6+1/6*8+.+1/2006*2008=(1/2*4)+(1/4*6)+(1/6*8)+..........+(1/2006*2008) 1/2*4+1/4*6+1/6*8+1/8*10.1/2006*2008 计算1/2*4+1/4*6+1/6*8+.+1/2002*2004+1/2004*2006 1+1+2+1+2+6+4+5+8等于 1/4+5/8+6/2=? 1,2,3,4,5,6,8 1×2×3×4×5×6×8 2/1+4/1+4/1+6/1+8/1+16/1+32/1=? 1,2,4,6, [2^4+1/4)(4^4+1/4)(6^4+1/4)(8^4+1/4)(10^4+1/4)】/[1^4+1/4)(3^4+1/4)(5^4+1/4)(7^4+1/4)(9^4+1/4)] 2+2+5+0+4+1+6+8+2+6