When n = 0,1,2,3, the nth power of 2

When n = 0,1,2,3, the nth power of 2

When n = 0 ~ 3, the nth power of 2

Solving inequality 2 (x-3) (x + 2) - (x + 3) > (x + 1) (x-1)

2(x^2-x-6)-(x^2+6x+9)>x^2-1
x^2-8x-21>x^2-1
x

1 + 3 + 5 + 7 +... + 2N-1 = the square of a few

1+3+5+7+...+2n-1
Here we can use the summation formula of arithmetic sequence
Original formula = 1 / 2 * (1 + 2n-1) * n
=n^2
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1 / 3 square - 1 + 1 / 5 square - 1 + 1 / 7 square - 1 + 1 / (2n + 1) square - 1 + ＝（ ）

1 / (2n + 1) Square-1 = 1 / 2n (2n + 2) = 2 * [1 / 2N-1 / (2n + 2)]
Sum up
=2*[1/2+1/（2n+2）}