简便运算!好的追加100!题目在下面
50^2-49^2 48^2-47^2 ··· 4^2-3^2 2^2-1^2 =(50 49)(50-49) (48 47)(48-47) ··· (4 3)(4-3) (2 1)(2-1) =99 95 91 ··· 7 3 =(99 3)*25/2 =1275 20^2-18^2 16^2-14^2 ··· 4^2-2^2 =(20 18)(20-18) (16 14)(16-14) ··· (4 2)(4-2) =38*2 30*2 22*2 ··· 6*2 =2*(38 30 22 ··· 6) =2*(38 6)*5/2 =220 (1-1/2^2)(1-1/3^2)(1-...全部
50^2-49^2 48^2-47^2 ··· 4^2-3^2 2^2-1^2 =(50 49)(50-49) (48 47)(48-47) ··· (4 3)(4-3) (2 1)(2-1) =99 95 91 ··· 7 3 =(99 3)*25/2 =1275 20^2-18^2 16^2-14^2 ··· 4^2-2^2 =(20 18)(20-18) (16 14)(16-14) ··· (4 2)(4-2) =38*2 30*2 22*2 ··· 6*2 =2*(38 30 22 ··· 6) =2*(38 6)*5/2 =220 (1-1/2^2)(1-1/3^2)(1-1/4^2)*···*(1-1/11^2)(1-1/12^2) =(1 1/2)(1-1/2)(1 1/3)(1-1/3)(1 1/4)(1-1/4)*···*(1 1/11)(1-1/11)(1 1/12)(1-1/12) =1/2*3/2*2/3*4/3*3/4*5/4*···*10/11*12/11*11/12*13/12 =1/2*13/12 =13/24。
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