# Thread: Sum question,some confusion

1. ## Sum question,some confusion

hi everyone

Compute $\displaystyle S_5$for the following:
$\displaystyle \sum^\infty _{n=0} a_n$ if $\displaystyle a_n=n(n+1)(n+2)$

my working:
start from a1= 0=0(0+1)(0+2)=0
a2=1=1(1+1)(1+2)=6
a3=2=2(2+1)(2+2)=24
a4=3=3(3+1)(3+2)=60
a5=4=4(4+1)(4+2)=120

i am confused wheter the answer is 210 or 420. i started with a1(0) until a5(4).
i am confused,please advise. did i do it right,

thank you so much for your advice.

thank you in advance.

2. Dear anderson,

I do not get what you mean by if

But if your expression is ,

$\displaystyle a_1=1(2)(3)=6$

$\displaystyle a_2=2(3)(4)=24$

$\displaystyle a_3=3(4)(5)=60$

$\displaystyle a_4=4(5)(6)=120$

$\displaystyle a_5=5(6)(7)=210$

Therefore, $\displaystyle S_5=6+24+60+120+210=420$

Hope this helps.

3. Hi Sudharaka,

thank you so much for helping to clarify,now i understand.

thank you again.

4. Hi Sudharaka,

thank you so much for helping to clarify.the question is:
$\displaystyle \sum^\infty _{n=0} a_n$ if $\displaystyle a_n=n(n+1)(n+2)$
i missed a typo.

did i do it right???

thank you again.

5. Originally Posted by anderson
Hi Sudharaka,

thank you so much for helping to clarify.the question is:
$\displaystyle \sum^\infty _{n=0} a_n$ if $\displaystyle a_n=n(n+1)(n+2)$
i missed a typo.

did i do it right???

thank you again.
Dear anderson,

Do you want to calculate $\displaystyle \sum_{n=0}^{\infty}a_n$ or is it $\displaystyle \sum_{n=0}^{5}a_n$.

Because, $\displaystyle \sum_{n=0}^{\infty}a_n=\infty$

6. Hi Sudharaka

the question is compute $\displaystyle S_5$, the sum of 5

thank you & regards

7. Hi Sudharaka

the question is compute $\displaystyle S_5$, the sum of 5

Compute $\displaystyle S_5$for the following:
$\displaystyle \sum^\infty _{n=0} a_n$ if $\displaystyle a_n=n(n+1)(n+2)$

thank you & regards