1/2*6+1/4*8+1/6*10+...+1/2n*(2n+4)的极限
问题描述:
1/2*6+1/4*8+1/6*10+...+1/2n*(2n+4)的极限
答
1/2*6+1/4*8+1/6*10+...+1/2n*(2n+4)
=1/4(1/2-1/6)+1/4(1/4-1/8)+1/4(1/6-1/10)+.+1/4(1/2n-1/(2n+4))
=1/4(1/2-1/2n+4)
=1/8(1-1/n+2)
=(n+1)/8(n+2)
极限是 1/8