Let a>0, and z_{1}>0. Define z_{n+1}= sqrt(a+z_{n}), for n is a natural number. Show that {z_{n}} converges and find the limit.
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Originally Posted by TaTzRE66 Let a>0, and z_{1}>0. Define z_{n+1}= sqrt(a+z_{n}), for n is a natural number. Show that {z_{n}} converges and find the limit. 1. Prove that is an increasing sequence. 2. Prove that has an upper bound. According to a well known theorem, is convergent. If is its limit then, Solving this equation and taking into account that for all , you'll find
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