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3/1+15/1+35/1+63/1···+（2N+1)(2N+3)/1+···+8099/1

分类: 作业答案 • 2022-05-31 13:56:45
问题描述：

3/1+15/1+35/1+63/1···+（2N+1)(2N+3)/1+···+8099/1

答

3/1+15/1+35/1+63/1···+（2N+1)(2N+3)/1+···+8099/1
=[(1-3/1)/2]+[(3/1-5/1)/2]+[(5/1-7/1)/2]+[(7/1-9/1)/2]+...[(89/1-91/1)/2]
=(1-3/1+3/1-5/1+5/1-7/1+7/1-9/1+.+89/1-91/1)/2
=(1-91/1)/2
=(91/90)/2
=91/45

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