summation - The idea behind the sum of powers of 2
2016年10月29日 · There's a lot of visualisations of this out there. Write the numbers in base 2: The powers of 2 starting from 1 = 20 will be in binary, 1 + 10 + 100 + 1000 will always be a number that will be a n with all binary digits 1. This is the largest number having that many digits. SO it is of the form 2n + 1 − 1.
How to prove a formula for the sum of powers of $2$ by induction?
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polynomials - Stuck solving $z^2$ + $zw^*$= $18$ and …
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Lagrange multiplier to function - Mathematics Stack Exchange
2017年10月17日 · Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given condition: f(x, y, z) =x2 +y2 +z2; x4 +y4 +z4 = 1 f (x, y, z) = x 2 + y 2 + z 2; x 4 + y 4 + z 4 = 1. My solution: As we do in Lagrange multipliers I have considered ∇f = λ∇g ∇ f = λ ∇ g where g(x, y, z) =x4 +y4 +z4 g (x, y, z) = x 4 ...
linear algebra - If $A^2 = I$ (Identity Matrix) then $A = \pm I ...
Every matrix satisfying A2 = I is diagonalizable, because either it is ± I or its minimal polynomial is (x − 1)(x + 1). The general solution is obtained by taking all diagonal matrices with entries ± 1 on the diagonal and conjugating by invertible matrices. Jonas Meyer, this is only true if charF ≠ 2.
logarithms - Is there an approximation to the natural log function …
x-1 is a crude approximation that is good for values of x close to 1. 2*(x-1)/(x+1) is a better approximation with a larger range. 6*(x-1)/(1 + 4 * Sqrt(x) + x) is better and has an even larger range. 90*(x-1)/(7+32 * x^(1/4) + 12 * x^(1/2) + 32 * x^(3/4) + 7 * x) is even better and has a larger range, but it never exceeds 90 for any positive real value of x.
Is this correct method to prove that $a^2 + b^2 + c^2 ≥ ab + bc …
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how to convert 1e+11 into number? - Mathematics Stack Exchange
2017年1月14日 · 1 e+11 = 1 ×10+11 1 e+11 = 1 × 10 + 11. You should know that 10 10 raised to any positive integer is a 1 1 with that many 0 0 s behind it. So. 10+11 = 100000000000 10 + 11 = 100000000000. thank you for your reply. i might be able to accept your answer after 11mins (from now) as shown in SO msg.
Show that $|z+w|^2$ + $|z-w|^2$ = $2|z|^2 + 2|w|^2$
This question shows research effort; it is useful and clear. 4. Show that | z + w | 2 + | z − w | 2 = 2 | z | 2 + 2 | w | 2. Every time I work this problem out I have 2 | z | 2 but I can not get the other piece. Here is what I got so far. Let z = a + bi and w = c + di, then.
Sum of a series of a number raised to incrementing powers
2014年12月28日 · late to the party but i think it's useful to have a way of getting to the general formula. this is a geometric serie which means it's the sum of a geometric sequence (a fancy word for a sequence where each successive term is the previous term times a fixed number). we can find a general formula for geometric series following the logic below