Saved Bookmarks
| 1. |
Find the nth term&then obtain the sum of n terms of the series |
|
Answer» Answer: ∴n th term=n(n+1)(n+3) ∴ SUM = k=1 ∑ n
k(k+1)(k+3) = k=1 ∑ n
(k 3 +4k 2 +3K) = k=1 ∑ n
k 3 +4 k=1 ∑ n
k 2 +3 k=1 ∑ n
k [ 2 n(n+1)
] 2 + 6 4n(n+1)(2n+1)
+3 2 n(n+1)
= 4 n 2 (n+1) 2
+ 3 2n(n+1)(2n+1)
+ 2 3
n(n+1) =n(n+1)[ 4 n(n+1)
+ 3 n(2n+1)
2 3
] =n(n+1)[ 12 3n 2 +3n+16n+8+18
] = 12 n(n+1)+(3n 2 +19n+26)
Ans |
|