Question:

What would 1 cent per day doubled every day for 30 days equal?

Answer:

One cent per day, doubled every day for thirty days would equal $5,368,709.12 . That's a type of math problem called geometric progression!

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Geometric progression

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2. The sum of the terms of a geometric progression, or of an initial segment of a geometric progression, is known as a geometric series.

Thus, the general form of a geometric sequence is

Pi Penny Means
Mathematical analysis

Mathematical analysis is a branch of mathematics that includes the theories of differentiation, integration, measure, limits, infinite series, and analytic functions. These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry. However, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space).

Early results in analysis were implicitly present in the early days of ancient Greek mathematics. For instance, an infinite geometric sum is implicit in Zeno's paradox of the dichotomy. Later, Greek mathematicians such as Eudoxus and Archimedes made more explicit, but informal, use of the concepts of limits and convergence when they used the method of exhaustion to compute the area and volume of regions and solids. In India, the 12th century mathematician Bhāskara II gave examples of the derivative and used what is now known as Rolle's theorem.

A series is, informally speaking, the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely.

In mathematics, given an infinite sequence of numbers { an }, a series is informally the result of adding all those terms together: a1 + a2 + a3 + · · ·. These can be written more compactly using the summation symbol ∑. An example is the famous series from Zeno's dichotomy and its mathematical representation:


Coins of the United States

Coins of the United States dollar were first minted in 1792. New coins have been produced annually since then and they make up a valuable aspect of the United States currency system. Today, circulating coins exist in denominations of 1¢ (i.e. 1 cent or $0.01), 5¢, 10¢, 25¢, 50¢, and $1.00. Also minted are bullion (including gold, silver and platinum) and commemorative coins. All of these are produced by the United States Mint. The coins are then sold to Federal Reserve Banks which in turn are responsible for putting coins into circulation and withdrawing them as demanded by the country's economy.

Today four mints operate in the United States producing billions of coins each year. The main mint is the Philadelphia Mint, which produces circulating coinage, mint sets and some commemorative coins. The Denver Mint also produces circulating coinage, mint sets and commemoratives. The San Francisco Mint produces regular and silver proof coinage, and produced circulating coinage until the 1970s. The West Point Mint produces bullion coinage (including proofs). Philadelphia and Denver produce the dies used at all of the mints. The proof and mint sets are manufactured each year and contain examples of all of the year's circulating coins.

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