Proof by induction
Base case:
n=1: 1*2*3=6 is obviously divisible by six.
Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.
For n+1:
(n+1)(n+2)(n+3)=
(n(n+1)(n+2)+3(n+1)(n+2))
We have assumed that n(n+1)(n+2) is divisble by 6.
We now only need to prove that 3(n+1)(n+2) is divisible by 6.
If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.
The "cool" part about this proof.
Since n is a natural number greater than 1 we can say the following:
If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.
Answer:
9
Step-by-step explanation:
a^3=72900/100
a=(729)^1/3
a=9
Answer:
about 214.1
Step-by-step explanation:
Since pi r squared is the formula for a circle's area, you would do the opposite. First, you would divide 144001 by pi which is about 45,836.94. Then, you would find the square root of that which is about 214.1.
Answer:
Given - Triangle ABC
AD bisects BC ( I.e AB = AD)
To prove - Angle BAD = Angle CAD
Solution -
AB = AD (given)
Angle B = Angle C ( angle opposite to equal sides are also equal )
In a triangle BAD and CAD
AD = AD ( common)
angle B = Angle C ( prove above)
AB = AD = ( given )
By SAS congruence Triangle ABC is congruent to Triangle ABD
by CPCT BAD = CAD
hence, Proved
Answer:
Step-by-step explanation:
Given expression is 
.
Now we need to find the cube root of given expression .
![\sqrt[3]{27a^{12}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27a%5E%7B12%7D%7D)
![=\sqrt[3]{3*3*3a^{4*3}}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B3%5D%7B3%2A3%2A3a%5E%7B4%2A3%7D%7D)
![=\sqrt[3]{3^3\left(a^4\right)^3}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B3%5D%7B3%5E3%5Cleft%28a%5E4%5Cright%29%5E3%7D)
![=\sqrt[3]{\left(3a^4\right)^3}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B3%5D%7B%5Cleft%283a%5E4%5Cright%29%5E3%7D)
Since cube root and cube are opposite operations of each other. So they will cancel each other.
Hence correct choice is the last choice .
