题目内容
等差数列{an}中，a1=3，公差d=2，Sn为前n项和，求
+
+…+
．
| 1 |
| S1 |
| 1 |
| S2 |
| 1 |
| Sn |
∵等差数列{an}的首项a1=3，公差d=2，
∴前n项和Sn=na1+
d=3n+
×2=n2+2n(n∈N*)，
∴
=
=
=
(
-
)，
∴
+
+…+
=
[(1-
)+(
-
)+(
-
)+…+(
-
)+(
-
)]
=
-
．
∴前n项和Sn=na1+
| n(n-1) |
| 2 |
| n(n-1) |
| 2 |
∴
| 1 |
| Sn |
| 1 |
| n2+2n |
| 1 |
| n(n+2) |
| 1 |
| 2 |
| 1 |
| n |
| 1 |
| n+2 |
∴
| 1 |
| S1 |
| 1 |
| S2 |
| 1 |
| Sn |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 2 |
| 1 |
| 4 |
| 1 |
| 3 |
| 1 |
| 5 |
| 1 |
| n-1 |
| 1 |
| n+1 |
| 1 |
| n |
| 1 |
| n+2 |
=
| 3 |
| 4 |
| 2n+3 |
| 2(n+1)(n+2) |
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