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The sum of a sequence (Posted on 2004-12-14) Difficulty: 4 of 5
Find the sum of the sequence: x, 2x2, 3x3, 4x4, 5x5, ... , nxn.

See The Solution Submitted by Mohammad    
Rating: 3.4286 (7 votes)

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re: Solution | Comment 4 of 10 |
(In reply to Solution by Old Original Oskar!)

The following program evaluates the actual sum, my formula and O.O.O.'s formula for various x and n:

CLS
FOR x = 2 TO 5
  FOR n = 2 TO 5
    term = x: t = term
    FOR termNo = 2 TO n
     term = term * x
     t = t + termNo * term
    NEXT termNo
    PRINT x, n, t,
    PRINT (1 - (n + 1) * x ^ n + n * x ^ (n + 1)) / (x - 2 + 1 / x),
    f = x * (n * x ^ (n + 1) - (n + 1) * x ^ n + 1) / (x - 1) ^ 2
    PRINT f
  NEXT
  PRINT
NEXT

The results agree.  The columns below are x, n, the actual sum, my formula, O.O.O.'s formula:

2             2             10            10            10
2             3             34            34            34
2             4             98            98            98
2             5             258           258           258
3             2             21            21            21
3             3             102           102           102
3             4             426           426           426
3             5             1641          1641          1641
4             2             36            36            36
4             3             228           228           228
4             4             1252          1252          1252
4             5             6372          6372          6372
5             2             55            55            55
5             3             430           430           430
5             4             2930          2930          2930
5             5             18555         18555         18555

  Posted by Charlie on 2004-12-14 18:28:11
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