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Bernoulli's inequality by induction

I'm proving Bernoulli's inequality by induction but I noticed something strange. See wikipedia proof: http://en.wikipedia.org/wiki/Bernoulli's_inequality Notice how they multiply both sides of the ...
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Integer solutions to an ellipsoid surface

Given the equation $$x^2+2y^2+5z^2+xz =n$$ where $n$ is any positive integer, what is the smallest odd integer for which no integer solution $(x,y,z)$ exists (i.e. $x,y,z$ are integers)? I know that ...
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Relating to $( a ^ b ) + c = d$ and $( a ^ b ) - c = d$

Is there a way of deducing the smallest integer values for $a, b$ and $c$ that satisfy either $( a ^ b ) + c = d$ or $( a ^ b ) - c = d$ such that the addition $( a + b + c )$ is the smallest ...
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Approximating a probability distribution given multiple datasets

I am beginner in mathematics/statistics and apologise in advance for my faulty use of language. I am working on a problem in statistical genetics. Given a dataset, $D$, I obtained probabilities for ...
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Financials Maths- Credited Interest

You invest £1,000 in an account for 5 years at 9% pa nominal. How much will you get at the end of the 5 years if the interest is is credited: a) annually; b) 6 monthly; c) 3 monthly; ...
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Fix $T > 0.$ Let $V \subset H \subset V^*$ be a Gelfand triple. Consider the linear parabolic PDE $$u_t - Au = f\quad\text{in L^2(0,T;V^*)}$$ $$u(0) = u_0$$ where $u_0 \in H$ and $f \in ... 1answer 56 views Trouble with fixed point iteration. Find the fixed point(s) of$g(x) = (1/2)x^2 + (1/2)x$. Does the fixed point iteration(s) converge(s) to the the fixed point(s) if you start with a close enough approximation? Then choose$x_0 ...
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Let G be a group. A subgroup H is called characteristic if $f(H)\subset H$ for all auto morphism $f$ of G.Pick out true statements. (a) Every characteristic subgroup is normal. (b) Every normal ...
Find: $$\int_{-\infty}^\infty\int_{-\infty}^\infty e^{-(3x^2+2\sqrt{2}xy+3y^2)}\,dxdy$$ I have no idea how to solve this,I would be thankful, if someone help me to solve this Thank you.