2 years ago

I don’t know how to do this.

Mathematics

1 answer:

sashaice [31]2 years ago

5 0

Answer:

Step-by-step explanation:

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Prove by mathematical induction that 1+2+3+...+n= n(n+1)/2 please can someone help me with this ASAP. Thanks

Iteru [2.4K]

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:

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

Which terminates the proof, since we showed that

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

as required

4 0

2 years ago

Need as much help as I can get before 7 minutes are over

andriy [413]

Answer:

think the answer is E but not 100%. been a while. let me know either way

7 0

3 years ago

-8x = -96 <br> (a)-14 <br> (b) -13<br> (c)-12<br> (D) 12

Leto [7]

Answer:

D) 12

Step-by-step explanation:

divide each term by -8 and simplify

-8/-8x=-96/-8

x=12

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2 years ago

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Jayda is watching a movie that lasts 1 hour and 37 minutes. She has watched 52 minutes so far. How many minutes are left in the

Svetlanka [38]

Answer:

45 minutes

Step-by-step explanation:

97-52 = 45

5 0

3 years ago

At tire depot , a pair of new tires sells for $216. The managers special advertises the same tires at a rate of $380 for 4 tires

Fittoniya [83]

A pair of tires is $216, so at that rate 4 tires would be $432. The managers special is $380 so $432-$380=$52 savings for 4. $52\4=$13 savings per tire.

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2 years ago