数列问题1-1/3+1/2-1/4+1/3-1/5……1/n-1/n+2=?这种题到底怎么列项啊?

Question

数列问题1-1/3+1/2-1/4+1/3-1/5……1/n-1/n+2=?这种题到底怎么列项啊?

Answer 1

1-1/3+1/2-1/4+1/3-1/5……1/n-1/n+2
=1+1/2+1/3+1/4+.+1/(n+2)-[1/3+1/4+1/5+.+1/(n-1] .把带加号的和带减号的分开.
=1+1/2+ 1/n +1/(n+1) +1/(n+2) .把相同的项消掉
=3/2 + 1/n +1/(n+1) +1/(n+2).最后得出结果.