hey, your inequality should be corrected as >= 1372 otherwise your range will not fall within ans.choices 1)-4) and must be above 350, namely n=512

S=[a(1)+a(n)]*n/2 where a(1)=cubic root(1)=1 and a(n)=cubic root(n)

by letting n(1+cubic root(n))>=2778 we have n=521, cubic root(n)=8
but if the inequality has >=1372 then it's exactly n=343

oldheaven wrote:what is the minimum range of "n" corresponded to this inequality:

" [cubic root of 1]+[cubic root of 2]+...+[cubic root of n]>=1389 "

1)between 250 and 260
2)between 300 and 310
3)between 320 and 330
4)between 340 and 350

In this question you are not dealing with an Arithmetic progression to use that formula.Be careful.
the "[]" means greater integer meaning ,for example, If 0<x<1 then [x]=0 and if 1<x<2 then [x]=1 and so on.

S=[a(1)+a(n)]*n/2

[] in my post notation are additional parentheses only

if we aren't dealing with sequence then how we get the totals? hm, i may be wrong

oldheaven wrote:In this question you are not dealing with an Arithmetic progression to use that formula.Be careful.
the "[]" means greater integer meaning ,for example, If 0<x<1 then [x]=0 and if 1<x<2 then [x]=1 and so on.

S=[a(1)+a(n)]*n/2

oldheaven wrote:what is the minimum range of "n" corresponded to this inequality:

" [cubic root of 1]+[cubic root of 2]+...+[cubic root of n]>=1389 "

1)between 250 and 260
2)between 300 and 310
3)between 320 and 330
4)between 340 and 350

The value of the greatest integer function of each number will depend on which two successive perfect integer cubes the number falls between.

[cube root of n] for 1<=n<8 is 1

[cube root of n] for 8<=n<27 is 2

[cube root of n] for 27<=n<64 is 3

[cube root of n] for 64<=n<125 is 4

[cube root of n] for 125<=n<216 is 5

[cube root of n] for 216<=n<343 is 6

The sum of the series for n=215 is 1(7)+2(19)+3(37)+4(61)+5(91)=855. The sum of the numbers whose cube roots have a greatest integer of 6 is 6(127)=762. 762+855=1587, which is larger than 1389, so the value of n must be such that 216<=n<343. To find out how many 6's we need, solve the following inequality:

855+6x>=1389

6x>=534

x>=89

We need 89 such terms, plus the 215 that gave us 855, so n=89+215=304.

So the answer is 2

you are such a meticulous and attentive guy.thank you.