 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Sum Greatest And Least Roots (Posted on 2008-05-22) Derive a formula for evaluating the following expression in terms of p and its higher powers, given that p is a positive integer.
```   Σ  ([3√m] + <3√m>)
m=1 to p3
```
Note: [x] is the greatest integer ≤ x, and <x> is the least integer ≥ x

 See The Solution Submitted by K Sengupta No Rating Comments: ( Back to comment list | You must be logged in to post comments.) re: answer Comment 3 of 3 | Verified gives the same answers:

`1             2             22             24            243             120           1204             380           3805             930           9306             1932          19327             3584          35848             6120          61209             9810          981010            14960         1496011            21912         2191212            31044         3104413            42770         4277014            57540         5754015            75840         7584016            98192         9819217            125154        12515418            157320        15732019            195320        19532020            239820        239820`
`DEFDBL A-ZCLSFOR p = 1 TO 20 t = 0 FOR i = 1 TO p * p * p   cr = INT(i ^ (1 / 3) + .5)   IF cr * cr * cr <> i THEN cr = i ^ (1 / 3)   t = t + INT(cr) - INT(-cr) NEXT PRINT p, t, p * (p + 1) * (3 * p * p - 3 * p + 2) / 2NEXT`
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 Posted by Charlie on 2008-05-23 00:10:42 Please log in:

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