求和符号的数学题,是怎样计算的?2010 1∑ n(n+1)n=1
2019-04-02
求和符号的数学题,是怎样计算的?
2010 _1___
∑ n(n+1)
n=1
优质解答
2010 _1___
∑ n(n+1)
n=1
2010 1 1
= ∑ --- - ----
n=1 n n+1
=1-1/2+1/2-1/3+……+1/2010-1/2011
=1-1/2011
=2010/2011
2010 _1___
∑ n(n+1)
n=1
2010 1 1
= ∑ --- - ----
n=1 n n+1
=1-1/2+1/2-1/3+……+1/2010-1/2011
=1-1/2011
=2010/2011