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# Math problem?

Evaluate: [(1*2*4+2*4*8+3*6*12+.....)/(1*3*9+2*6*18+3*9*27+....)]^(1/3)

I found this in a facebook group and the answer is 2/3. But if I input this in wolfram, the answer 1.

### 3 Answers

- KrishnamurthyLv 71 month ago
[(1*2*4 + 2*4*8 + 3*6*12 +.....) / (1*3*9 + 2*6*18 + 3*9*27+....)]^(1/3)

= [(8 + 64 + 216 +.....) / (27 + 216 + 729 +....)]^(1/3)

= [(2^3 + 4^3 + 6^3 + ....) / (3^3 + 6^3 + 9^3 + ...)]^(1/3)

= (2 + 4 + 6 + ....) / (3 + 6 + 9 + ...)

= 2/3 + 2/3 + ......

= 2/3

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- AlanLv 71 month ago
Wolfram Alpha did not correctly understand the ellipses.

if you enter

[(1*2*4+2*4*8+3*6*12)/(1*3*9+2*6*18+3*9*27)]^(1/3) it says = 2/3

if you enter

[(1*2*4+2*4*8+3*6*12+4*8*16 + 5*10*20 )

/(1*3*9+2*6*18+3*9*27+ 4*12*36 +5*15*45 )]^(1/3)

= 2/3

but when you add the ellipse

it doesn't really understand what you mean

If you can write it as summation , I expect Wolftram Alpha

will get the right answer (I was wrong, it couldn't handle the

summation , said undefined) .

But does not seem to follow the ellipses.

- AlanLv 71 month agoReport
So what do the ellipse imply "..." goes on forever or ... goes on to the nth value

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- 1 month ago
x * 2x * 4x => 8x^3

x * 3x * 9x => 27x^3

So what you have is:

(8 * 1^3 + 8 * 2^3 + 8 * 3^3 + 8 * 4^3 + .... + 8 * n^3) / (27 * 1^3 + 27 * 2^3 + 27 * 3^3 + .... + 27 * n^3) =>

(8/27) * (1^3 + 2^3 + 3^3 + 4^3 + ... + n^3) / (1^3 + 2^3 + ... + n^3) =>

(8/27) * 1 =>

(8/27)

(8/27)^(1/3) =>

2/3

Without knowing how exactly how you did the input in wolfram, it's impossible for me to demonstrate where you went wrong.

It gets it wrong with the

"..." ellipses are being used.

I am not sure you should expect it to understand exactly what they meant by

"..." anyway- Login to reply the answers