Answer: No, it can never be greater. At most it can be equal though.
5-1 x 20=56/56 x 90/56 54/67=67
Proving a relation for all natural numbers involves proving it for n = 1 and showing that it holds for n + 1 if it is assumed that it is true for any n.
The relation 2+4+6+...+2n = n^2+n has to be proved.
If n = 1, the right hand side is equal to 2*1 = 2 and the left hand side is equal to 1^1 + 1 = 1 + 1 = 2
Assume that the relation holds for any value of n.
2 + 4 + 6 + ... + 2n + 2(n+1) = n^2 + n + 2(n + 1)
= n^2 + n + 2n + 2
= n^2 + 2n + 1 + n + 1
= (n + 1)^2 + (n + 1)
This shows that the given relation is true for n = 1 and if it is assumed to be true for n it is also true for n + 1.
<span>By mathematical induction the relation is true for any value of n.</span>
Answer:
See below.
Step-by-step explanation:
An outlier can affect the mean by a lot. For example, if my neighbor moves out and Bill Gates moves in (he would be a <u>super</u> outlier!), the mean annual income would increase enormously.
The median, on the other hand, would not change at all. The income in the middle is still the income in the middle; Gates' income would not budge the median.
