化简:1/1×4 + 1/4×7 + 1/7×10 +……+1/(3n-2)×(3n+1)

问题描述:

化简:1/1×4 + 1/4×7 + 1/7×10 +……+1/(3n-2)×(3n+1)

1/1×4 + 1/4×7 + 1/7×10 +……+1/(3n-2)×(3n+1)
=1/3(1-1/4+1/4-1/7+.+1/(3n-2)-1/(3n+1))
=1/3(1-1/(3n+1))
=1/3*3n/(3n+1)
=n/(3n+1)