An infinite series is a mathematical concept that represents the sum of an infinite number of terms. It is denoted as a sum of terms in the form of a1 + a2 + a3 + ... where a is a constant and n is the number of terms.
The sum of an infinite series is the limit of the partial sums of the series as the number of terms approaches infinity. In other words, it is the value that the series approaches as more and more terms are added.
An infinite series converges if the limit of the partial sums exists and is finite. It diverges if the limit does not exist or if it is infinite.
In an arithmetic series, each term is obtained by adding a constant value to the previous term. In a geometric series, each term is obtained by multiplying the previous term by a constant value. In both cases, the terms continue indefinitely.
The sum of an infinite series can be calculated using various methods, such as the formula for the sum of a geometric series or the ratio test for convergence. In some cases, it may not be possible to find an exact value for the sum, but an approximation can be obtained by adding a finite number of terms.