#$&*
course Mth 151
2/24 around 11:45
Question: `q001. There are seven questions in this set.
See if you can figure out a strategy for quickly adding the numbers 1 + 2 + 3 + ... + 100, and give your result if you are successful. Don't spend more than a few minutes on your attempt.
Answer: You can pair 1 and 100, 2 and 99, 3 and 98, 4 and 97, 5 and 96…………etc. it will give you 50 different ways to reach 101. Then we will times 50 by 101=5050. 3, Okay, 3
*********************************************
Question: `q002. See if you can use a similar strategy to add up the numbers 1 + 2 + ... + 2000.
Answer: 1 and 2000, 2 and 1999, 3 and 1998…………etc. This will give you 1000 ways to reach 2001. Then we will times 1000 by 2001=2,001,000. 3, Okay, 3
*********************************************
Question: `q003. See if you can devise a strategy to add up the numbers 1 + 2 + ... + 501.
Answer: We will pair up 1 and 501, 2 and 500, 3 and 499………etc. There are an uneven amount of numbers, but the middle number is 250.5. 250.5 will be times by 502= 125,766.
3, Okay, 3
*********************************************
Question: `q004. Use this strategy to add the numbers 1 + 2 + ... + 1533.
Answer: The same strategy will be used. 1 and 1533, 2 and 1532, 3 and 1531……etc. will be paired up. The numbers will =1534. 1533 is odd so we will go between numbers to get how many pairs it takes to make 1534. It takes 766.5 pairs, times that by 1534 and we get 1,175,811 as our final answer. 3, Okay, 3
*********************************************
Question: `q005. Use a similar strategy to add the numbers 55 + 56 + ... + 945.
Answer: We will group 55 and 945, 56 and 944, 57 and 943……….etc. We will get 1000 when we add the pairs together. Since 945 is also an odd number we will go in-between numbers to see how many pairs there are. There are 445.5 pairs, times that by 1000 and we get our answer, 445,500
*********************************************
Question: `q006. Devise a strategy to add the numbers 4 + 8 + 12 + 16 + ... + 900
Answer: On this problem we will pair 4 and 900, 8 subtract 4 from 900 and get 896, 12 and again, subtract 4 from 896 giving you 892……..etc. 896/ 4=224, we will at 1 to that and get 225 jumps. Divide 225 by 2 and get 112.5. Times that by what you get for your total when you add the pairs together, 904 and you will get the answer, which is 101700. 3, Okay, 3
*********************************************
Question: `q007. What expression would stand for the sum 1 + 2 + 3 + ... + n, where n is some whole number?
Answer: n+1 or n/2????? 1, I don’t understand what this problem is asking. Are we trying to find a way that the expression will always work out evenly???? Overall I can’t grasp the question, 3
"
@&
See my previous notes related to submitting complete documents.
*@