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blackmangotree
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#1
Guys i have to do this maths test and I literally have no idea what to do for ths question:
Expressions for consecutive triangular numbers are:
0.5n(n+1) and 0.5(n+1)(n+2)
prove that the sum of two consecutive triangular numbers is always a square number
thank you
Expressions for consecutive triangular numbers are:
0.5n(n+1) and 0.5(n+1)(n+2)
prove that the sum of two consecutive triangular numbers is always a square number
thank you
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Pangol
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#2
(Original post by blackmangotree)
Guys i have to do this maths test and I literally have no idea what to do for ths question:
Expressions for consecutive triangular numbers are:
0.5n(n+1) and 0.5(n+1)(n+2)
prove that the sum of two consecutive triangular numbers is always a square number
thank you
Guys i have to do this maths test and I literally have no idea what to do for ths question:
Expressions for consecutive triangular numbers are:
0.5n(n+1) and 0.5(n+1)(n+2)
prove that the sum of two consecutive triangular numbers is always a square number
thank you
It is better to write the 0.5 as 1/2 in both cases. Don't expand any brackets, factorise instead.
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blackmangotree
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#3
(Original post by Pangol)
Since the question asks you to prove something about the sum of consecutive triangular numbers, try adding together the expressions you are given and see what you can make of that. This is the kind of question where it isn't easy to see how it's going to work out, you just have to get stuck in.
It is better to write the 0.5 as 1/2 in both cases. Don't expand any brackets, factorise instead.
Since the question asks you to prove something about the sum of consecutive triangular numbers, try adding together the expressions you are given and see what you can make of that. This is the kind of question where it isn't easy to see how it's going to work out, you just have to get stuck in.
It is better to write the 0.5 as 1/2 in both cases. Don't expand any brackets, factorise instead.
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Pangol
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#4
(Original post by blackmangotree)
what do you mean by don't expand any brackets? because surely you need to expand brackets to add them together right?
what do you mean by don't expand any brackets? because surely you need to expand brackets to add them together right?
2(x + 3)(x - 4) + 6(x + 3)(x + 1) = 2(x + 3)[(x - 4) + 3(x + 1)] (since both terms have a factor of 2 and (x + 3)
= 2(x + 3)[x - 4 + 3x + 3)] (now you can expand the brackets in the last term, since there is no choice left)
=2(x + 3)(4x - 1)
This gives a nicely factorised final answer, which is what you will need here.
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