Mathematics, 18.11.2019 18:31 SmokeyRN
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.
Answers: 3
Mathematics, 20.06.2019 18:04
The gades foundation and hbm corporation are eager to donate generously to their favorite charities. the gades foundation donated $250 in the first month, and each month afterward their cumulative donation total increases by 100$ the hbm corporation donated $64, in the first month, and each month afterward their cumulative donation total increases by 75%. in which month will the hbm corporation's cumulative donation total first exceed the gades foundations' cumulative donation total?
Answers: 1
Mathematics, 21.06.2019 14:40
Which system of linear inequalities is represented by the graph? !
Answers: 1
Mathematics, 21.06.2019 15:00
Translate the word phrase into a math expression. 15 fewer than the product of 4 and a number. (pls immediately)
Answers: 2
Mathematics, 21.06.2019 17:30
One integer is 8 times another. if the product is 72, then find the integers
Answers: 2
Base case: the summation formula holds for n - 1 because both sides evaluate to 1/2. inductive step...
History, 21.04.2021 01:00
Mathematics, 21.04.2021 01:00
Mathematics, 21.04.2021 01:00
Mathematics, 21.04.2021 01:00
Mathematics, 21.04.2021 01:00
Arts, 21.04.2021 01:00
History, 21.04.2021 01:00
Mathematics, 21.04.2021 01:00
Mathematics, 21.04.2021 01:00