![dancemomsrule1](/avatars/27079.jpg)
dancemomsrule1
18.11.2019 •
Mathematics
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.
Solved
Show answers
More tips
- S Style and Beauty Learn how to tie a keffiyeh on your head like a pro...
- S Style and Beauty How to braid friendship bracelets?...
- F Food and Cooking Delight for Gourmets: How to Prepare Liver Pate...
- C Computers and Internet How to Learn to Type Fast?...
- H Health and Medicine Angina: Causes, Symptoms, and Treatment...
- D Dating, Love, Relationships How to Overcome Jealousy: Tips and Tricks...
- H Health and Medicine 10 Ways to Cleanse Your Colon and Improve Your Health...
- W Work and Career How to Start Your Own Business: Tips and Recommendations...
- F Food and Cooking How to Make Delicious Cabbage Pies: The Best Recipes!...
- F Food and Cooking Discover Delicious Recipes You Can Make with Ground Meat...
Answers on questions: Mathematics
- M Mathematics Rbp-ctxa-etx join join...
- M Mathematics A man shares his money between his sons, Cyrus and Peter in the ratio 4 : 9. If Cyrus share is GH¢100, find the amount shared and Peter s share....
- M Mathematics If x=4,y=2,z=1,p=3,q=0 then find value of 4qy ÷ 8px + yz plz answer correctly...
- M Mathematics Which triangle is similar to triangle pqr...
- M Mathematics Question 1 of 9 Which of the following is the equation of the quadratic function below? -10 10 10...
- M Mathematics Find the volume of the cylinder in terms of . h = 6 and r = 3.a. 27 in.³b. 108 in.³c. 54 in.³d. 324 in.³...
- M Mathematics Can someone please help me out....
- M Mathematics A ball is dropped from 248 feet above the ground level and after the second bounce it rises to the height of 62 feet. If the height to which the ball rises after...
- M Mathematics Which inequalities are true? Select the four correct answers. Square root of 5 2.3 square root of 6 Square root of 5 2.4 square root of 6 Square root of 4 Square...
- M Mathematics A jet travels 490 miles in 5 hours. At this rate, how far could the jet fly in 10 hours? What is the rate of speed of the jet?...
Ответ:
4(3m^3-2m^2+4m+2)
Step-by-step explanation: