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# 10 Comments

 Oct 6 comment Extention of vector bundles on projective line: $Ext^1({\mathcal O_{\mathbb{P}^1}}(n),{\mathcal O_{\mathbb{P}^1}}(m))=$?? Yes, I have. But I think that computation of $Ext^1% as extension is difficult. Are you agree? Aug 15 comment Prove that$ \frac{n}{\phi(n)} = \sum\limits_{d \mid n} \frac{\mu^2(d)}{\phi(d)} \mu(d)$and$\phi(d)$multiplicative. Hence$\sum_{d \mid n} \frac{\mu^2(d)}{\phi(d)}$also multiplicative. Left and right side are multiplicative. For$p^k$: $$\dfrac{p^k}{p^k-p^{k-1}}=1+\dfrac 1{p-1}$$ Aug 11 comment Summation of divergent series of Euler:$0!-1!+2!-3!+\cdots$"For every fixed i, identify the coefficient of xi in the LHS and in the RHS." - How can this be used? Aug 11 comment Summation of divergent series of Euler:$0!-1!+2!-3!+\cdots$Numerical calculations in maple: for$x=0.7, n=10$left-hand side is 0.6634301660, right-hand side is 0.6635102741. Aug 11 comment Summation of divergent series of Euler:$0!-1!+2!-3!+\cdots$$$\int\limits_0^{\infty}\dfrac{e^{-t}}{xt+1}dt=s_n(x)+o(x^n)$$ Aug 11 comment Graph isomorphism as permutation matrix.$\pi M=M\pi$is$M=\pi^{-1}M\pi$Aug 11 comment Graph isomorphism as permutation matrix. Why is not it obvious? Aug 10 comment Showing$f(x)=\sum_{n=1}^{\infty}{\sin\left(\frac{x}{n^2}\right)}$is continuous. Or$\sum_{k=N}^{\infty}sin(x/k^2)