Question

01

想請問第三小題2n的答案是如何算出來的謝謝

已知級數前n項的和aq+a+...+an=n²+n+3,求:
(1) a+at+a20 ° (2)90。 (3)a。(以n表之)
答
L
An = Sn - Sn-t
20 +20 + 3
510-59
=
423
#
100+10+3=113
81+9+3=93
h+h+3 - (n-1)² + (n-1) +3
= h²=h+3 - n = 24-1+2-1+3
= 5
113-93=20.
#
5, h = 1
an =
2n, h≥2

Answer 1

qn

aₙ=(a₁+a₂+⋯+aₙ₋₁+aₙ) - (a₁+a₂+⋯+aₙ₋₁) (n≥2)
=[n²+n+3] - [(n-1)²+(n-1)+3]
=[n²+n+3] - [n²-n+3]
= 2n