计算数列:1又1/2,4又1/4,7又1/8,10又1/6,.的前n项和
问题描述:
计算数列:1又1/2,4又1/4,7又1/8,10又1/6,.的前n项和
答
1又1/2+4又1/4+7又1/8+……+(3n-2)又1/2ⁿ
=(1+4+7+……+3n-2)+1/2+1/4+1/8+1/2ⁿ
=(1+3n-2)n/2+1/2×(1-1/2ⁿ)/(1-1/2)
=(3n-1)n/2+1/2ⁿ -1