求极限问题!求高手解答高数的问题
有界: 先证明 当 n >= 4, x_n = 4, x_n > -(1+5^(1/2))/2。
x_4 = -2^(1/2) > -(1+5^(1/2) )/2。
假设x_n > -(1+5^(1/2) )/2, 则
x_{n+1} = -(1-x_n)^(1/2) > -(1+ (1+5^(1/2))/2 )^(1/2)
= -((3+5^(1/2))/2 )^(1/2)
= -(1+5^(1/2) )/2。
即当 n >= 4, -(1+5^{1/2})/2 (x_n)^2 + x_n - 1 (x_n)^2 -x_n x_(n+1) a = -(1+5^{1/2})/...全部
有界: 先证明 当 n >= 4, x_n = 4, x_n > -(1+5^(1/2))/2。
x_4 = -2^(1/2) > -(1+5^(1/2) )/2。
假设x_n > -(1+5^(1/2) )/2, 则
x_{n+1} = -(1-x_n)^(1/2) > -(1+ (1+5^(1/2))/2 )^(1/2)
= -((3+5^(1/2))/2 )^(1/2)
= -(1+5^(1/2) )/2。
即当 n >= 4, -(1+5^{1/2})/2 (x_n)^2 + x_n - 1 (x_n)^2 -x_n x_(n+1) a = -(1+5^{1/2})/2 因为 a < 0。
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