作业帮数列求和,
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 20:48:51
数列求和,
数列求和,
数列求和,
Sn=[(1+3¹)/2¹]+[(1+3²)/2²]+[(1+3³)/2³]···+[(1+3ⁿ)/2ⁿ]
=(1/2¹+3¹/2¹)+(1/2²+3²/2²)+(1/2³+3³/2³)···+(1/2ⁿ+3ⁿ/2ⁿ)
=(1/2¹+1/2²+1/2³+···+1/2ⁿ)+(3¹/2¹+3²/2²+3³/2³+···+3ⁿ/2ⁿ)
=[(1/2¹)/(1-1/2)](1-1/2ⁿ)+[(3¹/2¹)/(1-3/2)](1-3ⁿ/2ⁿ)
=(1-1/2ⁿ)+(3ⁿ⁺¹/2ⁿ-3)
=3ⁿ⁺¹/2ⁿ-1/2ⁿ-2
和式=S
=lim(n↝+∞)Sn
=lim(n↝+∞)[3ⁿ⁺¹/2ⁿ-1/2ⁿ-2]
=+∞-0-2
=+∞
正无穷，求和式不收敛