简便运算!好的追加100!题目在下面
2个回答
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
