作业帮高一数列一道,求第二问具体过程,
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高一数列一道,求第二问具体过程,
高一数列一道,求第二问具体过程,
高一数列一道,求第二问具体过程,
an=2n
Sn= (n+1)n
1/Sn = 1/[(n+1)n] = 1/n - 1/(n+1)
bn=1/S(n+1)+1/S(n+2)+...+1/S(2n)
= [1/(n+1) -1/(n+2)] + [1/(n+2) -1/(n+3)]+...+[1/(2n) -1/(2n+1)]
= 1/(n+1) - 1/(2n+1)<...
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an=2n
Sn= (n+1)n
1/Sn = 1/[(n+1)n] = 1/n - 1/(n+1)
bn=1/S(n+1)+1/S(n+2)+...+1/S(2n)
= [1/(n+1) -1/(n+2)] + [1/(n+2) -1/(n+3)]+...+[1/(2n) -1/(2n+1)]
= 1/(n+1) - 1/(2n+1)
let
f(x)= 1/(x+1) - 1/(2x+1)
f'(x) = -1/(x+1)^2 +2/(2x+1)^2 =0
(2x+1)^2 - 2(x+1)^2=0
2x^2-1=0
x= √2/2 (max)
max bn =b1=1/2 - 1/3 =1/6
min k = 1/6
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