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 increases by
n each time.
use induction to prove that
d(n)= n(n+1)/2
part A: prove the statement is true for n=1
part B: Assume that the statement is true for n=k + 1, therefor proving it true for all natural numbers, n.
hint* since the total number of dots increase by n each time, prove that d(k) + (k+1) = d (k+1)
*please answer i really need help!!
1 answer:
Answer:
<h3>Part A</h3>
- d(n) = n(n + 1)/2
- n = 1 ⇒ d(1) = 1(1 + 1)/2 = 2/2 = 1, proved
<h3>Part B</h3>
- d(k) + (k + 1) =
- k(k + 1)/2 + (k + 1) =
- [k(k + 1) + 2(k + 1)]/2 =
- [(k + 1)(k + 1 + 1)]/2 =
- d(k + 1)
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