Counting to 1,000,000

[anoni]

14453.
(-1) x 4 + sqrt(4) + 5 = 3

Here's a question.
Prove via Mathematical induction that 1 x 5 + 2 x 6 + 3 x 7 + ... + n(n + 4) = (1/6)n(n + 1)(2n + 13) for n => 1
Step 1. Assume n = 1
LHS = 1(1 + 4) = 5
RHS = (1/6)1(1 + 1)(2 + 13) = 30/6 = 5
LHS = RHS therefore true for n = 1

Step 2. Assume n = k, k =>1
1 x 5 + 2 x 6 + 3 x 7 + ... + k(k + 4) = (1/6)k(k + 1)(2k + 13)

Step 3. Assume n = k + 1, k => 1
1 x 5 + 2 x 6 + 3 x 7 + ... + k(k + 4) + (k + 1)(k + 5) = (1/6)(k + 1)(k + 2)(2k + 15)
LHS = 1 x 5 + 2 x 6 + 3 x 7 + ... + k(k + 4) + (k + 1)(k + 5)
LHS = (1/6)k(k + 1)(2k + 13) + (k + 1)(k + 5)
LHS = (1/6)(k + 1)[k(2k + 13) + 6(k + 5)]
LHS = (1/6)(k + 1)(2k^2 + 13k + 6k + 30)
LHS = (1/6)(k + 1)(2k^2 + 19k + 30)
LHS = (1/6)(k + 1)(k + 2)(2k + 15)
LHS = RHS

Step 4.
Thus proven by mathematical Induction.

[MrRazot]

14454


-1^(4+5)+5=4


lol looks fun.
if i whipped out my maths book i may even understand it on my own terms

[anoni]

14455
1 x 4 - 4 + 5 = 5

This is another one that I've just done, got the correct answer. Turning off music helps with maths apparently

Two points P(2ap, ap^2) and Q(2aq, aq^2) are on the parabola x^2 = 4ay.
The normal to P is given by x + py = 2ap + ap^3 and the normal to Q is given by x + qy = 2aq + aq^3.
The point R is the intersection of the normals to P and Q. Find R.

My working:
1) x = 2ap + ap^3 - py
2) x = 2aq + aq^3 - qy
2ap + ap^3 - py = 2aq + aq^3 - qy
2ap - 2aq + ap^3 - ap^q + qy - py = 0
2a(p - q) + a(p^3 - q^3) + y(q - p) = 0
2a(p - q) + a(p - q)(p^2 + 2pq + q^2) = y(p - q)
[Divide everything by (p - q)]
y = 2a + a(p^2 + 2pq + q^2)
y = a(p^2 + 2pq + q^2 + 2)
(y co-ordinate found)

1) y = 2a + ap^2 - x/p
 2) y = 2a + aq^2 - x/q
2a + ap^2 - x/p = 2a + aq^2 - x/q
2ap + ap^3 - x = 2ap + aq^2p - xp/q
2apq + ap^3q - xq = 2apq + aq^3p - xp
2apq - 2apq + ap^3q - aq^3p - x(p - q) = 0
apq(q^2 - p^2) = -x(q - p)
apq(q - p)(q + p) = -x(q - p)
[Divide everything by (q - p)]
apq(p + q) = -x
x = -apq(p + q)
[x co-ordinate found]

Therefore R = [-apq(p + q), a(p^2 + 2pq + q^2 + 2)]

And that was correct

[MrRazot]

14456
1 + 4 - 4 + 5 = 6
lol


i enjoy listening to music while studying
i'm sure i would be able to understand that with a diagram


screw this i'll be a municipal worker...

[anoni]

14457
1 x 4 - sqrt(4) + 5 = 7

I do too, but I've just noticed that since I turned the music off I'm getting everything right

and the question didn't come with a diagram nor did I draw one...
...though I probably should

[MrRazot]

14458


1^4 + sqrt(4) + 5 = 8


im not great at maths, but when i draw a diagram... <poo> gets real

[Kyriin]

14459

...

My brain after trying to comprehend Anoni's math: aasdfghj

[MrRazot]

14460


1 x sqrt(4) + 4 - 6 = 0


Study = No Fail
No Study = Fail


therefore: Study + No Study = Fail + No Fail
                 Study(1 + No) = Fail(1 + No)
                 Study(1 + No) = Fail(1 + No)

therefore: Study = Fail
therefore: No Study = No Fail

[Kyriin]

14461

I am too tired to make sense of this.

[MrRazot]

14462


((-1+4)x4)/6=2


lol n00b

[Kyriin]

14463

14+4≠63

AWYEA.

[WingedZephyr]

14464

I will not do maths. >8C

[Kyriin]

14465

Yes, yes you will! >83

[MrRazot]

14466

1^(4-4)x6=6
WZ... YUNO DO MATHS 

[WingedZephyr]

14467

Maths are lame!