I don't either it is quite hard to be fair
Let
In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:
So, the base case is ok. Now, we need to assume 
and prove 
.
states that
Since we're assuming , we can substitute the sum of the first n terms with their expression:
Which terminates the proof, since we showed that
as required
Answer:
7.8
Step-by-step explanation:
9514 1404 393
Answer:
a.
Step-by-step explanation:
For an even-index radical, ...
![\sqrt[n]{x^n}=|x|\qquad\text{n even}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5En%7D%3D%7Cx%7C%5Cqquad%5Ctext%7Bn%20even%7D)
This lets us simplify the given expression as follows:
![\sqrt[4]{81x^6y^4}-|y|\sqrt[4]{x^6}-\sqrt[4]{16x^2}=\sqrt[4]{(3xy)^4x^2}-|y|\sqrt[4]{x^4x^2}-\sqrt[4]{2^4x^2}\\\\=3|xy|\sqrt[4]{x^2}-|xy|\sqrt[4]{x^2}-2\sqrt[4]{x^2}=\boxed{2|xy|\sqrt[4]{x^2}-2\sqrt[4]{x^2}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B81x%5E6y%5E4%7D-%7Cy%7C%5Csqrt%5B4%5D%7Bx%5E6%7D-%5Csqrt%5B4%5D%7B16x%5E2%7D%3D%5Csqrt%5B4%5D%7B%283xy%29%5E4x%5E2%7D-%7Cy%7C%5Csqrt%5B4%5D%7Bx%5E4x%5E2%7D-%5Csqrt%5B4%5D%7B2%5E4x%5E2%7D%5C%5C%5C%5C%3D3%7Cxy%7C%5Csqrt%5B4%5D%7Bx%5E2%7D-%7Cxy%7C%5Csqrt%5B4%5D%7Bx%5E2%7D-2%5Csqrt%5B4%5D%7Bx%5E2%7D%3D%5Cboxed%7B2%7Cxy%7C%5Csqrt%5B4%5D%7Bx%5E2%7D-2%5Csqrt%5B4%5D%7Bx%5E2%7D%7D)
Explanation:
The angles are <em>vertical angles</em> if the opposites of the rays forming one of the angles are the rays forming the other angle.
More formally, if V is the common vertex, and ...
- R is a point on one of the rays forming Angle 1
- S is a point on the ray that is the opposite of ray VR
- T is a point on the other ray forming Angle 1
- U is a point on the ray that is the opposite of ray VT
Then angle RVT and angle SVU are vertical angles.
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Another way to say this is that points R, V, S are collinear, as are points T, V, U, and the two angles of interest are RVT and SVU.
If the above conditions cannot be met, then the angles are not vertical angles.
