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2007 iTest Problems/Problem 58

Revision as of 03:52, 8 October 2014 by Timneh (talk | contribs) (Created page with "== Problem == Let <math>T=\text{TNFTPP}</math>. For natural numbers <math>k,n\geq 2</math>, we define <cmath>S(k,n)=\left\lfloor\frac{2^{n+1}+1}{2^{n-1}+1}\right\rfloor+\left\lfl...")
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Problem

Let $T=\text{TNFTPP}$. For natural numbers $k,n\geq 2$, we define \[S(k,n)=\left\lfloor\frac{2^{n+1}+1}{2^{n-1}+1}\right\rfloor+\left\lfloor\frac{3^{n+1}+1}{3^{n-1}+1}\right\rfloor+\cdots+\left\lfloor\frac{k^{n+1}+1}{k^{n-1}+1}\right\rfloor\] Compute the value of $S(10,T+55)-S(10,55)+S(10,T-55)$.

Solution

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