化簡2/1!+2/3!+…+n/(n+1)! 1/2!+2/3!+…+n/(n+1)!

化簡2/1!+2/3!+…+n/(n+1)! 1/2!+2/3!+…+n/(n+1)!


第一個是1/2!
n/(n+1)!
=[(n+1)-1]/(n+1)!
=(n+1)/(n+1)!-1/(n+1)!
=1/n!-1/(n+1)!
所以=1/1!-1/2!+……+1/n!-1/(n+1)!
=1-1/(n+1)!



這個怎麼化簡?3^n - 3^(n-1)


原式=3^n-(3^n



3的N次减去3的N-1次化簡下來


3^N-3^(N-1)
=3^(N-1)*(3-1)
=2*3^(N-1)