Question

Bài này khó nè các bn làm hộ mk nha
  *tính tổng
1.3+3.5+5.7+ . . . +(2n+1)(2n+3)

(chú ý:dấu chấm biểu thị phép nhân, làm bài này theo công thức tổng quát)

Answer 1

[(2n+1)(2n+2)(2n+3)(2n+4):12]+(n+1)

Answer 2

\(A=1.3+3.5+5.7+...+\left(2n+1\right)\left(2n+3\right)\)

\(6A=1.3.\left(5+1\right)+3.5.\left(7-1\right)+5.7.\left(9-3\right)+...+\left(2n+1\right)\left(2n+3\right)\left(2n+5-2n+1\right)\)

\(6A=3+1.3.5-1.3.5+3.5.7-3.5.7+5.7.9-...-\left(2n-1\right)\left(2n+1\right)\left(2n+3\right)\)

\(+\left(2n+1\right)\left(2n+3\right)\left(2n+5\right)\)

\(6A=\left(2n+1\right)\left(2n+3\right)\left(2n+5\right)+3\)

\(A=\frac{\left(2n+1\right)\left(2n+3\right)\left(2n+5\right)+3}{6}\)