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:
7
Step-by-step explanation:
Answer:
38.4
38.4 is 48% of 80
Step-by-step explanation:
What is 48% of 80?
Y is 48% of 80
Equation: Y = P% * X
Solving our equation for Y
Y = P% * X
Y = 48% * 80
Converting percent to decimal:
p = 48%/100 = 0.48
Y = 0.48 * 80
Y = 38.4
Answer:
56/81
Step-by-step explanation:
8/9 * 7/9 = 56/81 of total plants
The correct option is the last one. h is negative and k is positive.
<h3>
What can we say about h and k?</h3>
For the absolute value function:
g(x) = |x - h| + k
We know that the vertex is on the point (h, k).
On the graph, we can see that the vertex is on the point (-2, 1), then we have:
h = -2
k = 1
So the sign of h is negative and the sign of k is positive. The correct option is the last one.
If you want to learn more about absolute value functions:
brainly.com/question/1782403
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