- #1
Feynmanfan
- 129
- 0
Could anybody please tell me how to do this?
Σn/[(n+1)(n+2)(n+3)]
Thanks!
Σn/[(n+1)(n+2)(n+3)]
Thanks!
Feynmanfan said:Still can't solve it. My computer says it certainly converges to 1/4. How can I prove that?
it cannot be representing a coefficient in the form of Σd*(a1-an)matt grime said:<acronym title='Loop Quantum Gravity' style='cursor:help;'>LGQ</acronym>, you can't take that term outside the summation as the n is part of the summation index.
To find the sum of n/[(n+1)(n+2)(n+3)], we can use the telescoping series method. We start by writing out the first few terms of the series, and then we use partial fraction decomposition to simplify the expression. After that, we take the limit as n approaches infinity to find the sum.
The telescoping series method is a technique used to simplify infinite series by eliminating most of the terms. This is achieved by writing out the first few terms of the series and then using partial fraction decomposition to simplify the expression. The remaining terms will then "cancel out" or "collapse" into a simpler expression, making it easier to find the sum.
Partial fraction decomposition is a method used to simplify rational expressions by breaking them down into simpler fractions. This is done by writing the expression as a sum of simpler fractions with distinct denominators. This technique is helpful in simplifying expressions and solving for unknown variables.
We take the limit as n approaches infinity to find the sum of the series because we are dealing with an infinite number of terms. This means that we need to find the value of the series as n gets larger and larger, approaching infinity. By taking the limit, we are essentially finding the "end behavior" of the series, which gives us the sum.
Yes, the sum can also be found by using other methods such as the geometric series method or the ratio test. However, the telescoping series method is often the most efficient and straightforward way to find the sum of this particular series. It is also a commonly used technique in mathematics and is worth understanding and practicing.