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60000 < 43³
x³ < 180000
53³ < 180000
x = 43, 53
55) p = (1²-2²)+(3²-4²)+(5²-6²)+ ... + (2009²-2010²)+2011²
p = (1-2)(1+2)+(3-4)(3+4)+(5-6)(5+6)+ ... + (2009-2010)(2009+2010)+2011²
p = (-1)(3) + (-1)(7) +(-1)(11) + ... + (-1)(4019)+ 2011²
p = -3 - 7 - 11 - ... - 4019 + 2011²
p = Sn + 2011²
a = -3
b = -7-(-3)
= -4
Un = -4019
Un = a+(n-1) b
-4019 = -3+(n-1) (-4)
-4016 = (n-1) (-4)
n-1 = -4016 / -4
= 1004
n = 1005
Sn = 1/2 n (a +U₁₀₀₅)
= 1/2 .1005. (-3- 4019)
= 1/2. 1005. (-4022)
= 1005. (-2011)
p = Sn + 2011²
= -1005. 2011 + 2011²
= 2011 (-1005 + 2011)
= 2011 (1006)
= 2023066