简算1+3/2+5/4+7/8+9/16+...+4003/2^2001
来源:百度知道 编辑:UC知道 时间:2024/07/04 13:40:18
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S = 1+3/2+5/4+7/8+9/16+...+4003/2^2001
两端同时乘 1/2
S/2 = 1/2 + 3/4 + 5/8 + 7/16 + 9/32 + …… + 4001/2^2001 + 4003/2^2002
两式相减
S - S/2
= 1 + (3/2 - 1/2) + (5/4 - 3/4) + (7/8 - 5/8) + …… + (4003/2^2001 -4001/2^2001) - 4003/2^2002
S/2 = 1 + 2*(1/2 + 1/4 + 1/8 + …… + 1/2^2001) - 4003/2^2002
= 1 + 2 * (1/2) * [1 - (1/2)^2001]/(1 -1/2) - 4003/2^2002
= 1 + 2 * ( 1 - 1/2^2001) - 4003/2^2002
= 3 - 1/2^2000 - 4003/2^2002
= 3 - 1/2^2000 * ( 1 + 4003/2^2)
= 3 - 4007/2^2002
S = 6 - 4007/2^2001
1+3/2+5/4+7/8+9/16+...+4003/2^2001
=1*2002+[(1/2)^0+(1/2)^1+……+(1/2)^2001]
=2002+[1*(1-1/2)^2001]
=2002+(1/2)^2001
6
1/1*2*3+1/2*3*4+1/3*4*5+.....
1/2*3+1/3*4+1/4*5+.....+1/100*101+
1/2+1/3+1/4+1/5+.......+1/10
1/2+1/3+1/4+1/5+...+1/100
1/2+1/3+1/4+1/5******+1/2004=?
1/2×1/3×1/4×1/5×…×1/2008
-1/2 1/2 -3/8 1/4 -5/32 ( )?
1/1*3+1/2*4+1/3*5+...+1/48*50
1/1*3+1/2*4+1/3*5+......+1/2005*2007
1/1*2+1/2*3+1/3*4+1/4*5+...+1/1999*2000