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:
These parallel lines cross 1 line. Because they are parallel they will form the same angles on that line. Therefore, x+50 = 3x-100 since those angles are corresponding angles made by a pair of parallels.
To find x we need to find what value of x gives the same answer for 3x-100 and x+50 since those 2 angles are equal.
x+50 = 3x-100 - now all we need to do is solve for x:
x+50 = 3x-100
50=2x-100
150=2x
75=x
x=75
Step-by-step explanation:
Answer: 37
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
1518 divided by 26 is 58 remainder 10.
... 1518 = 26×58 + 10 = 1508 + 10
Mr. Stephens will make 58 trips with a full load. After that, 10 tons of rock will remain.
If you do 1800 divided by 300, the answer is 6 hours.
