In the song 12 nights of Christmas each day the number of presents increases by that day's number...?

Question

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.

Answer 1

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

Answer 2

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.

Answer 3

No one present per day