1234+1=25=5@:2345+1=121=11@;345*6+1=361=19@.(n+1)(n+

学习时间:2026-06-04 06:46:16 阅读：1840

1*2*3*4+1=25=5@:2*3*4*5+1=121=11@;3*4*5*6+1=361=19@.(n+1)(n+2)(n+3)(n+4)+1=?@是平方

诚心的小天鹅

2026-06-04 06:46:16

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(n+1)(n+2)(n+3)(n+4)+1
=(n^2+5n+4)(n^2+5n+6)+1
=(n^2+5n+5-1)(n^2+5n+5+1)+1
=(n^2+5n+5)^2-1+1
=(n^2+5n+5)^2