Find an expression for the sum of the series

In summary, the problem is to find an expression for the sum of the series (1x2x6) + (2x3x7) + ... + n(n + 1)(n + 5) and give the answer as a product of linear factors in n. The attempt at a solution involved computing the first 5 terms of the series and dividing each sum by n to look for a pattern, but no solution was found. The numbers in the series all have a highest common denominator of 6, but this does not seem to be the solution.
  • #1
MegaDeth
83
0
1. Homework Statement

(1x2x6) + (2x3x7) + ... + n(n + 1)(n + 5)



2. Homework Equations

Find an expression for the sum of the series. Give your answer as a product of linear factors in n.


3. The Attempt at a Solution

I haven't tried it since I don't know what to do.
 
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  • #2
why don't you compute the first 5 terms of the series and see if you notice a pattern

n=1 sum=12
n=2 sum=54
n=3 ...

then divide each sum by n and see if you can find a pattern in terms of n
 
  • #3
Ok, so I have:

12/n + 42/n + 96/n + 180/n + 300/n

All I can see is that each number has a highest common denominator of 6, but I'm guessing that's not it.
 

FAQ: Find an expression for the sum of the series

1. What is a series?

A series is a mathematical expression that represents the sum of a sequence of numbers or terms. It can be finite or infinite and is written in the form of Σ (sigma) notation.

2. How do you find the expression for the sum of a series?

To find the expression for the sum of a series, you can use various methods such as the geometric series formula, telescoping series, or the method of partial sums. It depends on the type of series and its pattern.

3. What is the difference between a convergent and divergent series?

A convergent series is one where the sum of all its terms approaches a finite number as the number of terms increases. On the other hand, a divergent series is one where the sum of its terms approaches infinity or does not have a finite sum.

4. Can all series be summed to a finite number?

No, not all series can be summed to a finite number. Some series, such as the harmonic series, have an infinite sum. It is important to determine if a series is convergent or divergent before trying to find its sum.

5. How can finding the sum of a series be useful in real life?

Finding the sum of a series can be useful in various fields such as finance, economics, and physics. It can help calculate compound interest, evaluate the value of investments, and model real-life situations such as population growth or radioactive decay.

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