Simplify the formula (- 3) ^ (2n + 1) + 2 (- 3) ^ (2n)

Simplify the formula (- 3) ^ (2n + 1) + 2 (- 3) ^ (2n)

(-3)^(2n+1)+2(-3)^(2n)
=(-3)(-3)^2n+2(-3)^(2n)
= -(-3)^2n

1+2+3+4+… +(n-1) = 1 / 2n (n-1) according to what is the formula reduced to 1 / 2n (n-1)?

Let s = 1 + 2 + 3 + 4 + +(n-1) ① then s = (n-1) + (n-2) + (n-3) + (n-4) +. + 1 ② ∵ 1 + (n-1) = 2 + (n-2) = 3 + (n-3) = 4 + (n-4) =. = (n-1) + 1 then ① + ②, on the right side is n-1 n ∵ 2S = (n-1) n, i.e. s = (n-1) n / 2, i.e. 1 + 2 + 3 + 4 + +（n-1）=1/2n（n-1）...

Known is a non-zero root of the equation x & # 178; - 2005 + 1 = 0. Find the value of M & # 178; - 2004m + M & # 178; + 1 / 2005

A nonzero root of the equation x & # 178; - 2005x + 1 = 0;
x²-2005x+1=0;x²+1=2005x
2005/(x²+1)=x
m²-2004m+2005/(m²+1)=m²-2004m+m=m²-2005m=-1