人教a版選修2-2223數(shù)學(xué)歸納法2-展示頁(yè)
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【正文】 = .1 3 3 5 ( 2 k 1 ) ( 2 k + 1 ) 4 k + 2則當(dāng) n=k+1時(shí) , 2 2 2 22 2 22221 2 k ( k + 1 )+ + …+ +1 3 3 5 ( 2 k 1 ) ( 2 k + 1 ) ( 2 k + 1 ) ( 2 k + 3 )k + k ( k + 1 ) k ( k + 1 ) ( 2 k + 3 ) + 2 ( k + 1 )= + =4 k + 2 ( 2 k + 1 ) ( 2 k + 3 ) 2 ( 2 k + 1 ) ( 2 k + 3 )( k + 1 ) ( 2 k + 3 k + 2 k + 2 ) ( k + 1 ) ( 2 k + 1 ) ( k + 2 )==2 ( 2 k + 1 ) ( 2 k + 3 ) 2 ( 2 k + 1 ) ( 2 k + 3 )k + 3 k + 2 ( k + 1 ) + ( k + 1 )==4 k + 6 4 ( k +.1 ) + 2故當(dāng) n=k+1時(shí) ,結(jié)論也正確 . 根據(jù) (1)、 (2)知 ,對(duì)一切正整數(shù) n,結(jié)論正確 . (1)當(dāng) n=1時(shí) ,由上面
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