course Mth 151
6/20 10
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.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
You would pair 1 with 100, 2 with 99 and 3 with 98 since there are 100 numbers that add up to be 101 and the number of pairs is half of the total elements you would do 50*101= 5050
3
Ok
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Question: `q002. See if you can use a similar strategy to add up the numbers 1 + 2 + ... + 2000.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Pair 1 with 2000 and 2 with 1999 since there are 2000 elements there are 1000 pairs and the sume of 1+2000= 2001 and the sum of 2+1999=2001 you would do 2001*1000 and the answer would be 2,001,000
3
Ok
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Question: `q003. See if you can devise a strategy to add up the numbers 1 + 2 + ... + 501.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Pair 1 with 501 and 2 with 500 the number of pairs is 250.5 so you would do 250.5* 502= 125,766
1
Explain how since there are only 501 elements and the sum of pairing equals 502 that one element would have to be left out and explain how you figure out which element is left.
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Question: `q004. Use this strategy to add the numbers 1 + 2 + ... + 1533.
Your solution:
You start off by pairing 1 and 1533 and 2 with 1532 and 3 with 1531, then you divide 1533 by two and get 766.5 pairs and multiply that to the sum 1534 and get 1,175,811
3
Ok
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Question: `q005. Use a similar strategy to add the numbers 55 + 56 + ... + 945.
Your solution:
55 +945= 1,000 945/2= 472.5 so 1,000*472.5= 472,500
3
I did not compensate for the set not starting with 1 so I needed to figure out the 1 unit jumps which would have been 945-55=891 and then divide that by two to see how many pairs there are.
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Question: `q006. Devise a strategy to add the numbers 4 + 8 + 12 + 16 + ... + 900.
Your solution:
4 with 900= 904 but then you need to figure out the one unit jumps so you do 900-4= 896 and divide that by two to see the number of pairs 448 then you multiply that by 904 and get 404,992
3
The number jumped from 4 to 8 so I needed to divide 896 by 4 not two
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Question: `q007. What expression would stand for the sum 1 + 2 + 3 + ... + n, where n is some whole number?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
You would pair 1 with n 2 with n-1 3 with n-2 and see that they all equal n+1 they are n number therefore they are 2/n so the expression would be 2/n*(n+1)
3
ok
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