Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
In the song 12 nights of Christmas each day the number of presents increases by that day's number...?
and the number of presents you already had. For instance, on the first day you have one, on the second day you have 2+1=3, on the third day you have 3+3=6. How many presents do you have at the end of the twelve days, and for n number of days of Christmas how many presents do you have? Prove by induction.
3 Answers
- 1 decade agoFavorite Answer
well here's your answer 1+2+3+4+5+6+7+8+9+10+11+12=78 wow 78 presents in 12 days i hope that answers your question if u need anymore math help email me below
Source(s): slidingruin@yahoo.com - 1 decade ago
First getting formula:
Total gifts on nth day = toatl gifts on (n-1)th day + n.
S(n) = S(n-1) + n.
It is arithmetic series formula for sum of n numbers. So it follows that n(n+1)/2 presents on the nth' day. So after 12 days 12*13/2 =78 gifts in total.
Proving by induction:
Induction base: n = 1, on first day you have 1(1+1)/2 = 1 gift.
Induction Step: Assume it is true for n = k, so on kth day you have k(k+1)/2 gifts.
On (k+1)th' day, you will have k(k+1)/2 + (k+1) gifts = (k/2+1)(k+1) = (k+1)(k+2)/2 gifts.
S(k+1) is also same. So proved for (k+1)th day using kth day gifts.
And hence induction base and step are proved, so is our formula.
