You're solution is much shorter than mine. How did you do it? I don't know much about triangular numbers. I separated 1010100 into = 10002 + 1002 + 102. I noticed the pattern that n^2=a_{n}+a_{n-1}
So then I proved that: [\frac{n(n+1)}{2}]+[\frac{(n-1)n}{2}]=n^2
Afterwards, it was easy...
Homework Statement
Solve for x and y:
x2 + (√8)x*sin[(√2)xy] +2 = 0
Homework Equations
The Attempt at a Solution
Other than decomposing the root 8 i don't know what else to do. any hints? thanks.
Not exactly because you're not doing the same operations on both the equations. You're multiplying 10 for the x^2 and adding 10 for the other. If you had done the same operation on both functions then the outcomes would have also been the same.
Homework Statement
2sin(4x)-sin(2x)-(√3)cos(2x)=0
x is [0,2π]
Homework Equations
The Attempt at a Solution
Using trig identities:
8sinxcos3x-6sinxcosx-√3(2cos2x-1)
Please help me with this problem. I have no idea where to go from here. Thanks.
Homework Statement
-sin x = √3 * cos x
where x is [0,2π]
Homework Equations
The Attempt at a Solution
Would it be wrong to square both sides and then factor?
sin2 x = 3cos2 x
1-cos2 x = 3cos2 x
0= 4cos2 x - 1
0 = (2cos x -1)(2cos x + 1)
Now I solve the factors (2 solutions...
Homework Statement
Which terms of this sequence add up to 1010100? (Don't need to be consecutive terms)
{an}∞n=1 = {n(n+1)/2}∞n=1
Homework Equations
The Attempt at a Solution
The sequence is made up of the sums of all the numbers less than and including n. Don't really know much more...