Can You help me with this math question.. ( 10th grade level)?
pic 1
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pic 2
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pic 3
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question 1 asys how many rows and columns..
pic 1, has 2 and 2,, pic 2 has 3 and 3 pic 3 has 4 and 4
Q number 2 says total dots..
pic 1.. has 3 pic 2 has 6 pic 3 has 10
than #4 ( number 3 dont matter)
asks
can you develope a formula for the number of dots in an image with “x” rows?? Explain why this formula works..
i know how to get it
if there is 3 rows,,,
u find out the total by adding all the numbers before it including 3
like 1 +2+3 = 6 which is the total number of it if it had 3 rows ( see pic 2)
if there is 8 rows u go
1+2+3+4+5+6+7+8 = the total but dont knwo hwo to put that using a variable..
check ur solution by predicting the numbers of dots in an image with 10 row ( after u put 10 in place of ‘x’ u should get 55)
Favorite Answer
to prove it, proceed by induction. for your base case n=1, obviously n(n+1)/2 equals 1. now for our inductive step, n(n+1)/2 + (n+1) equals (n+1)(n+2)/2 which is of the form n(n+1)/2 for n+1 so our induction is complete.
=n(n+1)/2
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