Base case: the summation formula holds for n - 1 because both sides evaluate to 1/2. inductive step: suppose we already know for some arbitrary positive integer n that sigma ^n _k = 1 1/k)k + 1) = 1 - 1/n + 1. by adding the quantity 1/(n + 1)(n + 2)) to both sides, we get sigma ^n + 1 _k = 1 1/k(k + 1) = 1 - 1/n + 1 + 1//(n + 1)(n + 2) = 1 - n + 2 - 1//(n + 1)(n + 2) = 1 - n + 1//(n + 1)(n + 2) = 1 - 1/n + 2 thus, the summation formula holds for the case n + 1. this is the best of all the proofs in this quiz because it is not only correct, but also succinct and readable. it does not burden the reader with the unnecessary notational abstraction of a "p(n)". it's not ok in the base case to just state that both sides evaluate to 1/2. a proper informal proof must explain every last detail, even the details of basic arithmetic. an inductive proof is wrong if it does not refer to the statement to be proved as p(n). an inductive proof of a summation formula is not complete without a final declaration "thus, by the principle of mathematical induction, we have proved that the formula holds for all positive integers n." or words to that effect.

answer: median

step-by-step explanation:

the median is the middle value when a data set is ordered from least to greatest

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺