Discovering the Formula for Σ (i=1, n) √i

[EEristavi]

Homework Statement

Calculate Σ (i=1, n) √i

I want to write general formula, then use it for any n (like we have for Σ (i=1, n) i

Homework Equations

Σ (i=1, n) i = n (n+1) / 2
Σ (i=1, n) i^2 = n (n+1)(2n +1) / 6

The Attempt at a Solution

Comparing formulas provided above: I assume the answer must be: (n (n+1) / 2) * (3/(2n +1))

Is it correct? if yes how can I prove appropriately.

 

[mfb]

I don't understand your notation. What do the square brackets mean? I guess i[2] means i² = i^2, but what is i[1][/2]? The square root? $\sqrt i$?
If yes: No, your formula doesn't work.

 

[EEristavi]

Yes, it means √i. I tried to use "super script" function, but it didn't work as I see.

 

[EEristavi]

@mfb Can you give me a hint to get a correct answer?

 

[AspiringResearcher]

I highly doubt that your answer is correct because your answer is always a rational number, whereas the sum of square roots is not necessarily rational.

 

[mfb]

This is a much more difficult problem than the sum of some integer powers of numbers.
There is a formula, found by Ramanujan, but it needs some more work.

 

[EEristavi]

I highly doubt that your answer is correct because your answer is always a rational number, whereas the sum of square roots is not necessarily rational.

Yes, its incorrect.
It was kind of intuitive guess