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分数裂项6题要过程和答案,回答了后会再加分!第一题:3/1x2x3x4+3/2x3x4x5+……+3/17x18x19x20第二题:2/1x(1+2)+3/(1+2)x(1+2+3)+4/(1+2+3)x(1+2+3+4)+……+100/(1+2+……+99)x(1+2+……+100)第三题:3/1^2x2^2+5/2^2x3^2+7

题目详情
分数裂项6题
要过程和答案,回答了后会再加分!
第一题:3/1x2x3x4+3/2x3x4x5+……+3/17x18x19x20
第二题:2/1x(1+2)+3/(1+2)x(1+2+3)+4/(1+2+3)x(1+2+3+4)+……+100/(1+2+……+99)x(1+2+……+100)
第三题:3/1^2x2^2+5/2^2x3^2+7/3^2x4^2+……+15/7^2x8^2
第四题:3^2+1/3^2-1+5^2+1/5^2-1+7^2+1/7^2-1+……+1993^2+1/1993^2-1+1995^2+1/1995^2-1=________
第五题:2x2/1x3+4x4/3x5+6x6/5x7+8x8/7x9+10x10/9x11
第六题:1+1/1+2+1/1+2+3+……+1/1+2+……2007
至少要回答四题
只要回答第二题和第五题就行了
▼优质解答
答案和解析
第一题:3/1x2x3x4+3/2x3x4x5+……+3/17x18x19x20
=1/1x2x3-1/2X3x4+1/2x3x4-1/3x4x5+……+1/17x18x19-1/18x19x20
=1/1x2x3-1/18x19x20
=1/6-6840
=1139/6840
第二题:2/1x(1+2)+3/(1+2)x(1+2+3)+4/(1+2+3)x(1+2+3+4)+……+100/(1+2+……+99)x(1+2+……+100)
=1-1/(1+2)+1/(1+2)-1/(1+2+3)+1/(1+2+3)-1/(1+2+3+4)+……+1/(1+2+……+99)-1/(1+2+……+100)
=1-1/(1+2+……+100)
=1-1/5050
=5049/5050
第三题:3/1^2x2^2+5/2^2x3^2+7/3^2x4^2+……+15/7^2x8^2
=1/1^2-1/2^2+1/2^2-1/3^2+1/3^2-1/4^2+……+1/7^2-1/8^2
=1/1^2-1/8^2
=1-1/64
=63/64
第四题:3^2+1/3^2-1+5^2+1/5^2-1+7^2+1/7^2-1+……+1993^2+1/1993^2-1+1995^2+1/1995^2-1=1+2/3^2-1+1+2/5^2-1+1+2/7^2-1+……+1+2/1993^2-1+1+2/1995^2-1
=997+2/3^2-1+2/5^2-1+2/7^2-1+……+2/1993^2-1+2/1995^2-1
=997+2/2x4+2/4x6+2/6x8+……+2/1992x1994+2/1994x1996
=997+1/2-1/4+1/4-1/6+1/6-1/8+……+1/1992-1/1994+1/1994-1/1996
=997+1/2-1/1996
=997又997/1996
第五题:2x2/1x3+4x4/3x5+6x6/5x7+8x8/7x9+10x10/9x11
=1+1/1x3+1+1/3x5+1+1/5x7+1+1/7x9+1+1/9x11
=5+1/1x3+1/3x5+1/5x7+1/7x9+1/9x11
=5+1/2x(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=5+1/2x(1-1/11)
=5+5/11
=5又5/11
第六题:1+1/1+2+1/1+2+3+……+1/1+2+……2007
=2/2+2/6+2/12+……+2/2007x2008
=2x(1-1/2+1/2-1/3+1/3-1/4+……+1/2007-1/2008)
=2x(1-1/2008)
=2-1/1004
=1又1003/1004