Question

4*4/3*5+6*6/5*7+……+78*18/17*19用简便方法怎么做

Answer 1

4*4/3*5+6*6/5*7+……+18*18/17*19
=1+1/（3*5）+1+1/（5*7）+……+1+1/（17*19）
=8+0.5*（1/3-1/5+1/5-1/7+……+1/17-1/19）
=8+0.5*16/57
=8+8/57
=8又8/57

Answer 2

4*4/(3*5)+6*6/(5*7)+……+18*18/(17*19)
=4*4/[(4-1)*(4+1)]+6*6/[(6-1)*(6+1)]+……+18*18/[(18-1)*(18+1)]
=1+1/(4*4-1)+1+1/(6*6-1)+……+1+1/(18*18-1)
=8+[1/(3*5)+1/(5*7)+……+1/(17*19)]
=8+1/2(1/3-1/5+1/5-1/7+...+1/17-1/19)
=8+1/2(1/3-1/19)
=8又8/57

Answer 3

(4*4)/(3*5)=4^2/(4^2-1)=1+1/(4^2-1)=1+1/2*(1/3-1/5)
因此
原式=8+1/2*（1/3-1/5+1/5-1/7+...+1/17-1/19)
=8+1/2*(1/3-1/19)=8又8/57

Answer 4

你的提示不是错啦，最后是18*18/17*19