what is the sum of 1 to infinity
1 + 2 + 3 + 4 + ⋯ which increases without bound as n goes to infinity. Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum.
Exponentiation Any nonzero number raised to the 0 power is 1:[11]
1 + 2 + 3 + 4 + ⋯ Although the series seems at first sight not to have any meaningful value at all, it can be manipulated to yield a number of mathematically interesting results, some of which have applications in other fields such as complex analysis, quantum field theory, and string theory. Many summation methods are used in mathematics to assign numerical values even to a divergent series. In particular, the methods of zeta function regularization and Ramanujan summation assign the series a value of âˆ’1/12, which is expressed by a famous formula:[2]
Infinity In mathematics, "infinity" is often treated as a number (i.e., it counts or measures things: "an infinite number of terms") but it is not the same sort of number as either a natural or a real number.