here's my working
Hello!
I've got this problem.
18. Consider the following four equations:
1) 1 = 1
2) 2+3+4 = 1+8
3) 5+6+7+8+9 = 8+27
4) 10+11+12+13+14+15+16 = 27+64
Conjecture the general formula suggested by these four equations, and prove your conjecture.
Any help would be appreciated
Thanks!
Hello, BACONATOR!
Find the general statement is the biggest task . . .
Here's the pattern that I saw . . .18. Consider the following four equations:
Conjecture the general formula suggested by these four equations,
and prove your conjecture.
Equation 2: sum of 3 consecutive integers up to 2², equals 1³ + 2³
Equation 3: sum of 5 consecutive integers up to 3², equals 2³ + 3³
Equation 4: sum of 7 consecutive integers up to 4², equals 3³ + 4³
My conjecture:
Equation : sum of consecutive integers up to , equals
After a bit of algebra, I found that equation
. . has a sum that begins with
The sum is an arithmetic series with first term, ,
. . common difference, , and terms.
This sum is: .
. . which simplifies to: .
Hello, BACONATOR!
. .
The left side is an arithmetic series.
. . Its first term is:
. . The common difference is: ,
. . The number of terms is:
The sum is: .
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