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 Jun23 awarded Yearling Mar3 comment Invertible Matrix and Linearly Independent Vectors Proof That's right, yes. Feb27 answered Invertible Matrix and Linearly Independent Vectors Proof Feb26 comment Show that $\lim_{r \rightarrow 1} \sum_{n=1}^{\infty} r^{2^n}= \infty$ ... but using your inequality, for each $k\geq 1$, $$\lim_{r\to 1} \sum_{n=1}^\infty r^{2^n}\geq \lim_{r\to 1} kr^{2^k} = k,$$ so the result holds. Feb26 comment Show that $\lim_{r \rightarrow 1} \sum_{n=1}^{\infty} r^{2^n}= \infty$ But the condition $r^{2^k}\geq\frac12$ forces $k$ to be small, so we can't say that the sum is larger than something that gets arbitrarily large. Feb4 comment Evaluating $\int_\gamma z(1+|z|^2)^{-1/2}\,|dz|$ You have a small but crucial error here: $|t i e^{it}+e^{it}|=(1+t^2)^{1/2}$. Making this correction will simplify the integral. Jan22 comment How to find $\int_{0}^{1}\frac{1}{x^{2}+2x+2}\mathrm dx$ with contour integration The branch of $\log z$ required has a cut along the positive real axis - is that right? Nov2 awarded Nice Question Jun23 awarded Yearling Jun12 comment Show that $x=2\ln(3x-2)$ can be written as $x=\frac{1}{3}(e^{x/2}+2)$ @Lord_Farin - I disagree. This answer provides a useful hint that could allow the asker of the question to work the problem out for him/herself and so learn some maths in the process. Jun5 comment How to calculate this integral containing a Dirac delta function Hint: $$\delta(f(z_0))=\sum_{z_k:f(z_k)=0}\frac{\delta(z_0-z_k)}{|f'(z_k)|}.$$ See this link. May30 comment Can any planar graph have 4 vertices and 4 regions? @Ada - your last comment shows the importance of the definition of 'region' in the question. I think you should clear this up with your professor: he/she may be using a different definition to the one in Grimaldi et al. - or as you suggested originally, there may be a flaw in the question. May30 comment Can any planar graph have 4 vertices and 4 regions? ... so as you can see from the planar graph wikipedia page and from the wordpress source you've linked to, $K_4$ has only three regions (i.e. three areas that are enclosed by edges of the graph). May30 comment Can any planar graph have 4 vertices and 4 regions? I wonder is the version of $K_4$ you are thinking of the non-planar representation? See here and then here by way of contrast. May10 awarded Caucus Apr17 answered Shortest Vector for which Dot Product = x + 2y = 5. (Strang P21 1.2.26) Mar25 comment Complex Numbers Proof Typo in your second line. $|z|^2$ should be $|z|^2|w|^2$. Things should work out after that. Mar25 answered Prove that $|PC|^2 + |PD|^2 = |AB|^2$ if Mar21 comment Radius of Convergence for$S=\sum^{\infty}_{0}\frac{2^n(x-2)^n}{(n+2)!}$ You need to take the limit $n\to\infty$ in order to apply the test. Mar20 answered Finding nontrivial solutions to a system of equations