Mathematics, 03.09.2021 02:10 dria40
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)
Answers: 3
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