The first five triangular numbers are shown, where n represents the number of dots in the base of the figure, and d(n) represents the total number of dots in the figure.
When n = 1, there is 1 dot. When n = 2, there are 3 dots. When n = 3, there are 6 dots. Notice that the total
number of dots d(n) increases by n each time.

Use induction to prove that
d (n) = n(n+1)/2
Prove the statement is true for n = 1.

Part B:
Assume the statement is true for n=k. Prove that it must be true for n=k+1, therefore proving it true for all natural numbers, n.

hint: since the total number of dots increases by n each time, prove that d(k)+(k+1)=d(k+1)

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.

the answer is: d) o, f, and kr.

atomic radius of bromine (br) is 114 pm.

atomic radius of oxygen (o) is 73 pm.

atomic radius of fluorine (f) is 72 pm.

atomic radius of krypron (kr) is 112 pm.

the atomic radius of a chemical element is a measure of the size of its atom.

the atomic radius varies with increasing atomic number, but usually increases because of increasing of number of electrons.

the atomic radius decreases across the periods because an increasing number of protons, because greater attraction between the protons and electrons.