高中数列求和题,求学霸来帮我解答一下~

2025-05-19 17:44:49
推荐回答(3个)
回答1:

an=(a1+a2+...+an)-(a1+a2+...+a(n-1))
=(2^n-1)-[2^(n-1)-1]
=2^n-2^(n-1)
=2^(n-1)
(an)^2=4^(n-1)
(a1)^2+(a2)^2+...+(an)^2=(1-4^n)/(1-4)=(4^n-1)/3

回答2:

an = 2^n -1

(an)^2
= (2^n -1)^2
=2^(2n) -2^(n+1) + 1

a1^2+a2^2+...+an^2
=(4/3)[ 2^(2n) -1 ] - 4(2^n -1) + (1/2)n(n+1)

回答3: