根据1*2*3*4+4=25=5² 2*3*4*5+1=121=11² 3*4*5*6+1=361=19²,猜想(n+1)(n+2)(n+3)(n+4)+1=
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![根据1*2*3*4+4=25=5² 2*3*4*5+1=121=11² 3*4*5*6+1=361=19²,猜想(n+1)(n+2)(n+3)(n+4)+1=](/uploads/image/z/374195-11-5.jpg?t=%E6%A0%B9%E6%8D%AE1%2A2%2A3%2A4%2B4%3D25%3D5%26%23178%3B+2%2A3%2A4%2A5%2B1%3D121%3D11%26%23178%3B+3%2A4%2A5%2A6%2B1%3D361%3D19%26%23178%3B%2C%E7%8C%9C%E6%83%B3%28n%2B1%29%28n%2B2%29%28n%2B3%29%28n%2B4%29%2B1%3D)
根据1*2*3*4+4=25=5² 2*3*4*5+1=121=11² 3*4*5*6+1=361=19²,猜想(n+1)(n+2)(n+3)(n+4)+1=
根据1*2*3*4+4=25=5² 2*3*4*5+1=121=11² 3*4*5*6+1=361=19²,猜想(n+1)(n+2)(n+3)(n+4)+1=
根据1*2*3*4+4=25=5² 2*3*4*5+1=121=11² 3*4*5*6+1=361=19²,猜想(n+1)(n+2)(n+3)(n+4)+1=
(n+1)(n+2)(n+3)(n+4)+1
=[(n+1)(n+4)+1]²
=(n²+5n+5)²
(n+1)(n+2)(n+3)(n+4)+1=(n+1)(n+4)[(n+1)+1][(n+4)-1]+1
=(n+1)(n+4)[(n+1)(n+4)+2]+1
=[(n+1)(n+4)]²+2(n+1)(n+4)+1
=[(n+1)(n+4)+1]²
=(n²+5n+5)²
(n+1)(N+2)(N+3)(N+4)+1={(N-3)N+1}²