PLEASE HELP IM SO CONFUSED ON HOW TO DO THIS. Thanks if you can help. :P

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

natta225 [31]

5.33 Inches. I'd assume its C or the third one.

8 0

2 years ago

Korolek [52]

Answer:

3 dollars

Step-by-step explanation:

15 x .2

Because you convert the percentage to a decimal

3 0

2 years ago

vampirchik [111]

Answer:

2 out. of 7

Explanation:

First of all There are 2 C in the word and so it's going to be 2 out of the total number of words in the given word

2 / 7

So that is the probability 

8 0

2 years ago

Stella [2.4K]

Lines that are not in the same plane are called _____ lines. A. transversal B. parallel C. skew D. perpendicular
Answer: Skew

hope this helps :)

7 0

2 years ago