1*5/1+5*9/1+9*13/1+13*17/1+.45*49/1

上面是分子吧,应该是这样写：
1/1*5+1/5*9+...+1/45*49
=1/4[1-1/5]+1/4[1/5-1/9]+...+1/4[1/45-1/49]
=1/4[1-1/5+1/5-1/9+...+1/45-1/49]
=1/4*[1-1/49]
=1/4*48/49
=12/49

1/[n*(n+4)]=[1/n-1/(n+4)]/4
原式=[(1-1/5)+(1/5-1/9)+……+(1/45-1/49)]/4
=(1-1/49)/4
=12/49