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Differential Calculus

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8 Mar 2009 11:55:11 IST

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Unique Sequence

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Given a>0 and x0>0, show that there exists one and only one sequence of positive numbers such that

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apollo

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Joined: 21 Mar 2009

Posts: 345

1 May 2009 16:41:32 IST

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a good one.....

ak = n²+k where 0<=k<2n+1
S(a_k) = k and a_k+1=a_k+S(a_k) = n²+2k

and we can say a_k+1<= n²+4n

so the one and only perfect squares greater than n² and less than n²+2k is n²+2n+1

which is never equal to a_k+1.

apollo

Blazing goIITian

Joined: 21 Mar 2009

Posts: 345

2 May 2009 11:22:13 IST

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bhatt sir no comments?

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