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Illusion [34]
3 years ago
14

A cell phone provider offers a plan that costs $40 per month plus $0.10 per text message sent or received. A comparable plan cos

ts $70 per month but offers unlimited text messaging. How many text messages would have to be sent or received in order for the plans to cost the same each month? And if you send or receive an average of 100 text messages each month, which plan would you choose? Why?
Mathematics
1 answer:
anyanavicka [17]3 years ago
7 0
It would be 300 text message for the plan to cost the same each month
Mark as brainly
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Let

P(n):\ 1+2+\ldots+n = \dfrac{n(n+1)}{2}

In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:

P(1):\ 1 = \dfrac{1\cdot 2}{2}=1

So, the base case is ok. Now, we need to assume P(n) and prove P(n+1).

P(n+1) states that

P(n+1):\ 1+2+\ldots+n+(n+1) = \dfrac{(n+1)(n+2)}{2}=\dfrac{n^2+3n+2}{2}

Since we're assuming P(n), we can substitute the sum of the first n terms with their expression:

\underbrace{1+2+\ldots+n}_{P(n)}+n+1 = \dfrac{n(n+1)}{2}+n+1=\dfrac{n(n+1)+2n+2}{2}=\dfrac{n^2+3n+2}{2}

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P(n+1):\ 1+2+\ldots+n+(n+1) =\dfrac{n^2+3n+2}{2}

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