下面这两题怎样进行简便计算?1/1×3×5+1/3×5×7+……+1/11×13×151/3×1+1/4×2+1/5×3+……+1/22×20

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/17 19:29:15
下面这两题怎样进行简便计算?1/1×3×5+1/3×5×7+……+1/11×13×151/3×1+1/4×2+1/5×3+……+1/22×20下面这两题怎样进行简便计算?1/1×3×5+1/3×5×7

下面这两题怎样进行简便计算?1/1×3×5+1/3×5×7+……+1/11×13×151/3×1+1/4×2+1/5×3+……+1/22×20
下面这两题怎样进行简便计算?
1/1×3×5+1/3×5×7+……+1/11×13×15
1/3×1+1/4×2+1/5×3+……+1/22×20

下面这两题怎样进行简便计算?1/1×3×5+1/3×5×7+……+1/11×13×151/3×1+1/4×2+1/5×3+……+1/22×20
直接用公式F(N)=[(n+2)(n+4)]/n=n+6+8/n
n:1+2+3.11=(1+11)*11/2=66
6:6*11=66
8/n=8(1/n):8(1/1+1/2+1/3...1/11)=8*(ln(11) + 1)
所以和为140+ln11
第二个同理用n/(n+2)就行了