Recent content by Nobody1111

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    Graduate Convergence of Harmonic Series with Omitted 9s in Denominator

    In the harmonic series 1+1/2+1/3+1/4+... we omit expressions which contain digit 9 in denominator (so we omit e.g. 1/9, 1/19, 1/94, 1/893, 1/6743090 etc.). Proof that such series is convergent. Have You got any idea how to solve this problem? Thanks a lot for help
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    Graduate How to Prove the Determinant of a Cosine Matrix?

    Proof, that determinant (with n rows and columns) | cosx 1 0 0 ... 0 0 | | 1 2cosx 1 0 ... 0 0 | | 0 1 2cosx 1 ... 0 0 | | 0 0 1 2cosx ... 0 0 | = cos nx |...... | |...
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    Graduate Finding Limit of Sequence a_n with Parameter k

    One more question: What if k=-1. The limit doesn't exist or limit equals to infinity?
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    Graduate Finding Limit of Sequence a_n with Parameter k

    Find limit n-->infinity of sequence a_n: a_n = (1^k+2^k+...+n^k)/(n^(k+1)), where k is parameter. IThanks from advance for any help. I tried to compute this limit using Stolz Theorem, but I don't know if I can do it in this way.
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    Graduate Proof of Convergence of Sequences a_n and b_n

    Sequences a_n and b_n are defined in the follwing way: a_1=x; b_1=y; where 0<x<y and: a_(n+1) = (a_n+b_n)/2 b_(n+1) = sqrt(a_(n+1)+b_n) Proof, that both sequences are convergent to the same limit and find this limit. Thanks a lot for any help.