Have you studies arithmetic series before ? If you have you should without much difficulty be able to write down the formula for the sum of the first n odd numbers.
do you see how this relates to your problem ?
Hi, The question I have is:
Express a single generality that generalises all three related observations that
and show that your generalisation always holds true.
I know that the answer (i.e. RHS of =) is always (supposed to say no. of different terms)
I also know that LHS is , where a=1
but I'm not sure how to show all of this generally, so that it works for every case . Any ideas?
Hello, cozza!
bobak is absolutely correct . . . Did you catch his hint?
Express a single generality that generalises all three related observations that:
. .
and show that your generalisation always holds true.
Look at the left side:
. .
In general, we have: .
This is a arithmetic series with:
. . first term , common difference , and terms.
Its sum is: .
Hence, the sum of the first odd numbers is .[1]
Therefore, we have:
. .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Here is a visual "proof" of [1].
. .
. . . . . . . . . . . . . . . . . . .