limn趋近于无穷大(1+1/1+2+1/1+2+3……1/1+2+3+n)

题目

limn趋近于无穷大(1+1/1+2+1/1+2+3……1/1+2+3+n)

答案

1+1/1+2+1/1+2+3…+1/1+2+3+…+n
=2/1x2+2/2x3+2/3x4+…+2/n(n+1)
=2x[1-1/2+1/2-1/3+1/3-1/3+…+1/n-1/(n+1)]
=2x[1-1/(n+1)]
=2-2/(n+1)
lim (1+1/1+2+1/1+2+3……1/1+2+3+n)
n趋近于无穷大
=lim 【 2-2/(n+1)】
n趋近于无穷大
=2