利用极限存在准则证明题目。怎么做？
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a1=√2
for n>=2
an = √[2+a(n-1)]
{an } is increasing
an = √[2+a(n-1)]
(an)^2 = 2+a(n-1)
(an)^2 - a(n-1) - 2 =0
(an)^2 - an - 2 <0
(an -1/2)^2 < 5/2
√2 <an < (1+ √10)/2
{an} is bounded
=> lim(n->∞) an exists
for n>=2
an = √[2+a(n-1)]
{an } is increasing
an = √[2+a(n-1)]
(an)^2 = 2+a(n-1)
(an)^2 - a(n-1) - 2 =0
(an)^2 - an - 2 <0
(an -1/2)^2 < 5/2
√2 <an < (1+ √10)/2
{an} is bounded
=> lim(n->∞) an exists
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