1 + 3 + 5 + 7 +. + 2007 = the square of a few

1 + 3 + 5 + 7 +. + 2007 = the square of a few

According to the arithmetic sequence formula, the original formula = (1 + 2007) * 1004 / 2 = 1004 ^ 2
So the original formula is 1004 square

Using the formula of the sum of the first n terms of the equal ratio sequence to prove
a^n+a^(n-1)*b+a^(n-2)*b.+b=a^(n+1)-b^(n+1)/a-b

This series is the prime minister is a ^ n, the total ratio is B / A
Original formula = {a ^ n [1 - (B / a) ^ n + 1} (1-B / a)
=[a^n-(b^(n+1)/a]/[(a-b)/a]
=[a^(n+1)-b^(n+1)]/(a-b)

The proof process of the sum of the first n terms of the equal ratio sequence

Let Sn = a1 + A2 +... + an
Then QSn = A2 + a3 +... + an + 1
Then (1-Q) Sn = a1-an + 1 = n times of a1-a1 * Q
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