Please help meee(urgentttt)!!

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 :smile:

Reply 1

Pangol

15

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 :smile:

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.

Reply 2

blackmangotree

OP

11

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.

what do you mean by don't expand any brackets? because surely you need to expand brackets to add them together right?

Reply 3

Pangol

15

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?

Not at all. Suppose you were adding 2(x + 3)(x - 4) and 6(x + 3)(x + 1). Without expanding the brackets, you could do it like this:

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.

Please help meee(urgentttt)!!

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