1×1/5+1/5×1/9+1/9×1/13+······+1/37×1/41=?递等式简便运算,
问题描述：
1×1/5+1/5×1/9+1/9×1/13+······+1/37×1/41=?递等式简便运算,
答
1×1/5+1/5×1/9+1/9×1/13+······+1/37×1/41
=1/4×(1-1/5)+1/4×(1/5-1/9)+1/4×(1/9-1/13)+……+1/4×(1/37-1/41)
=1/4×(1-1/5+1/5-1/9+1/9-1/13+……+1/37-1/41)
=1/4×(1-1/41)
=1/4×40/41
=41分之10