spideyunlimit said:DO it again, you'll get 0^4 + n^4
Sigma notation is a mathematical notation used to represent sums. It is written as Σ followed by an expression, starting from an index value and ending at a limit value. For example, Σn=1 to 5 n^2 represents the sum of the squares of the numbers from 1 to 5.
Sigma notation allows for a compact and efficient representation of sums, making it easier to work with large sums and series. It also allows for the use of mathematical operations and functions within the expression. Sigma notation is commonly used in calculus, statistics, and other mathematical fields.
A telescopic problem in sigma notation is a type of sum where most of the terms cancel out, leaving only a few terms to be evaluated. This can be done by manipulating the expression to create a telescoping effect, where the terms collapse on each other and cancel out.
To solve a telescopic problem in sigma notation, you need to identify the pattern of terms that cancel out. This can be done by writing out a few terms and looking for a common factor or difference. Once the pattern is identified, you can use it to simplify the expression and evaluate the sum.
Sigma notation and telescopic problems have various real-world applications, such as in finance and economics for calculating compound interest and finding the present value of investments. They are also used in physics and engineering for calculating the total displacement or velocity of a moving object. Additionally, they can be used in statistics for calculating probabilities and in computer science for optimizing algorithms.