Ask your own question, for FREE!
Mathematics 17 Online
OpenStudy (anonymous):

The sum of the first n even positive integers is h. The sum of the first n odd positive integers is k. Then h - k = ? What would I do to solve this? How do I prove it? (the answer is: n)

OpenStudy (anonymous):

h=2+4+6+8+10...+n-4+n-2+n k=1+3+5+7+9...+n-5+n-3+n h-k=(2-1)+(4-3)+(6-5)+(8-7)+(10-9)+...+(n-4 - (n-5))+(n-2+(n-3))+n-n h-k=1+1+1+1+1...+1+1+1=n

OpenStudy (anonymous):

fan me if you understand :)

OpenStudy (anonymous):

The idea of the above is right, but the numbers at the end aren't correct. The first n positive even integers are 2, 4, 6, 8, ..., 2n. Those are the first n positive even integers. Note that the last one is 2n. So h = 2 + 4 + 6 + ... + 2n. The first 3 odd positive integers are 1, 3, 5. The first 5 odd positive integers are 1, 3, 5, 7, 9. The first 6 odd positive integers are 1, 3, 5, 7, 9, 11. What is the list of the first n odd positive integers? What does it end at? Can you see the pattern? If you list the first three, it ends at 2(3) - 1. If you list the first five, it ends at 2(5) - 1. ... If you list the first n, it ends at 2n - 1. So then k = 1 + 3 + 5 + ... + (2n - 1). Then h - k = 1 + 1 + ... + 1 as suggested above, and there are n ones since there are n terms. So h - k = n.

OpenStudy (anonymous):

Thank you very much :)

OpenStudy (anonymous):

indeed i was wrong :) but its great u understand :)

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
Countless7Echos: ik i'm late but finished ToT added some details :p
2 hours ago 2 Replies 0 Medals
Grimson: What's your new years resolution.
8 hours ago 1 Reply 1 Medal
LemmyluvsGelo: Why be sad when you could js be Gone . ud83dudd7a
7 hours ago 4 Replies 1 Medal
Ferrari: anyone have insta??
3 hours ago 23 Replies 3 Medals
xXAikoXx: I made art
12 hours ago 6 Replies 3 Medals
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!