Compute 1/1³ + 1/(1³+2³) + 1/(1³+2³+3³) + .... + 1/ (1³+2³+...30³)

[uneven crag]

If you don't understand the quotation (i.e the brackets and slash), I can send the image

[lofty swallow]

so , what have you tried ?

[uneven crag]

I tried using partial fractions

[lofty swallow]

then ?

[uneven crag]

Yeah that's it

Can't find a common factor

The denominators are 1,9,36,100 etc respectively

[lofty swallow]

what did you do in the first step ?

[uneven crag]

I summed the first 4 denominators, that is 1 + 1/9 + 1/36 + 1/100

Still trying to figure out another way though, it should be a telescoping series?

[lofty swallow]

yes it is

[uneven crag]

wait hold on
1 = 1 x 1
9 = 3 × 3
36 = 6 × 6
100 = 10 × 10
225 = 15 × 15

Wait let me retry

Wait nevermind

I need to find a matching factor

[lofty swallow]

your problem will be translated into that

[uneven crag]

Yes

[lofty swallow]

and you know the sum of cubes into n , right ?

[uneven crag]

(n(n+1)/2)²

And then?

[lofty swallow]

you can use partial fractions

[uneven crag]

Yes exactly that's what I did

Also what's the app you use?

To write that

[lofty swallow]

MathMagic Lite

btw , i dont think you need this question

the result of your problem is very long

[uneven crag]

Ok ty,

[lofty swallow]

No problem

[uneven crag]

Ok wait, let me look at the question again

I don't think the answer should be that complex

That's literally an octillion fraction

Oh wait that's indeed the question

Alright thanks again @lofty swallow

.close