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3 years ago

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There will be 1,398 students attending the assembly. During the assembly, our principal is going to be passing out 4 pieces of p

aper to each student. How many pieces of paper will the principal pass out at the assembly? *

1 answer:

Reika [66]3 years ago

8 0

Answer:

5592 pieces of paper

Step-by-step explanation:

Simple multiplication

1398(4)= 5592

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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

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Let

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

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

$P(n+1)$ states that

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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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