3 years ago

For 0 < x i will mark brainliest

Mathematics

1 answer:

Gemiola [76]3 years ago

4 0

Answer: I do not understand that....can you please restate your question?

Step-by-step explanation: I am very confused about this...

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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

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3 years ago

For each of these word problems, determine if the answer can be found using the division problem 125 ÷ 12.

olasank [31]

Answer:

125/12

Step-by-step explanation:

1st problem-no

2nd problem-yes

3rd problem-yes

4th problem-no

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3 years ago

A movie, including the previews, is 2 hours and 40

ra1l [238]

Answer:

7/8

Step-by-step explanation:

3 0

3 years ago

Jackson pays $18 per month for his phone service, plus $0.07 for each long distance minute used. Which of the following correctl

Ksenya-84 [330]

Its b, no matter what, he has to pay 18 dollars which effects the y intercept

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3 years ago

Read 2 more answers

Fred has a bakery. He sells 40 cakes in a day. If his sales increased by 120%, how many cakes will he sell in a day?

Nutka1998 [239]

You change 120% into a decimal, 1.20
then you multiply 1.2 by 40

Answer: 48 cakes Fred will sell a day

7 0

2 years ago