Stephanie Jones

46 reputation

1st year Maths student... and really there isn't anymore i need to say about myself and i should get back to studying...

	46 reputation	bio	website		visits	member for	6 months
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6 Questions

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3	Prove (*) by induction on k.
3	We define a sequence of rational numbers {$a_n$} by putting $a_1=3$ and $a_{n+1}=4-\frac{2}{a_n}$ for all natural numbers. Put $\alpha = 2 + \sqrt{2}$
1	Prove that $(e^{At}−I)/t→A$ as $t→0$, meaning $\\|(e^{At}−I)/t−A\\|\to 0$ as $t\to0$ for all $A\in C^{n×n}$.
1	Solve $x\equiv 2\pmod 5, x\equiv 1\pmod 8, x\equiv 7\pmod 9, x\equiv -3\pmod {11}$ for $x\in\mathbb Z$.
0	Compute $\phi(24)$. For each element $\mathbb Z /24$ decide whether the element is a unit or a zero divisor. [duplicate]

+15	Prove (*) by induction on k.
+5	Prove that $(e^{At}−I)/t→A$ as $t→0$, meaning $\\|(e^{At}−I)/t−A\\|\to 0$ as $t\to0$ for all $A\in C^{n×n}$.
+5	Solve $x\equiv 2\pmod 5, x\equiv 1\pmod 8, x\equiv 7\pmod 9, x\equiv -3\pmod {11}$ for $x\in\mathbb Z$.
-2	Compute $\phi(24)$. For each element $\mathbb Z /24$ decide whether the element is a unit or a zero divisor.

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