MaxWong

The wrong step is at the step n*(n+1) = 2n^2.

n * (n + 1) = n^2 + n instead.

\(n(n+1) = n^2 + n\)

\(n^2 + n = 20\\ n^2 + n - 20 = 0\\ (n+5)(n-4) = 0\\ n = -5(\text{rejected})\text{ or }n=4\)

Now that's correct.

Let a = arctan(\(\sqrt2 - 1\))

Double angle formulae:

\(\tan(2a)\\=\dfrac{2\tan a}{1-\tan ^2 a}\\=\dfrac{2(\sqrt2 - 1)}{1-(\sqrt2 - 1)^2}\\ = \dfrac{2\sqrt2 - 2}{1-(2+1-2\sqrt2)}\\ =\dfrac{2\sqrt2 - 2}{1-2-1+2\sqrt2}\\ =\dfrac{2\sqrt2 - 2}{2\sqrt2 - 2}\\ =1\)

When tan(2a) = 1, 2a = 45 degrees. Therefore a = 22.5 degrees or pi/8 radians.

8(arctan(sqrt(2)-1)) = 8(pi/8) = pi.

\(4xy^z+4=6\\ 4xy^z=2\\ xy^z=\dfrac{1}{2}\\ x=\dfrac{1}{2y^z}\\ y^z=\dfrac{1}{2x}\\ y = \dfrac{1}{\sqrt[z]{2x}}\\ z\log y = -\log (2x)\\ z = -\dfrac{\log2x}{\log y}\)

\(4\div{\dfrac{1}{5}}\\ =4\times 5\\ = 20\)

\(3\dfrac{1}{5 } +6\dfrac{2}{4}\\ = 3\dfrac{2}{10} + 6\dfrac{5}{10}\\ =9\dfrac{7}{10}\)

\(\dfrac{7}{8}-\dfrac{3}{4}\\ =\dfrac{7}{8}-\dfrac{6}{8}\\ =\dfrac{1}{8}\)

\(4-\dfrac{2}{4}\\ = 4-\dfrac{1}{2}\\ =3\dfrac{1}{2}\)

\(\text{You mean }\dfrac{1}{3}\text{ when you type 1/3. I know.}\)

I think Melody may know how to do this question. 

Sigh...... Already tried that few days ago...... Me not good at G.S. :(

Definitely 19.......

9 + 10 = 21 is wrong.

Main point: Silverfish is not a kind of fish.

Her calculator only perform calculations from left to right. It doesn't use BODMAS or PEDMAS.

This is what her calculator does.

52 + 8 x 2

= 60 x 2

= 120

Cube root of 216 is 6.

Use a^(1/n) for the n-th root of a.