# Probably a geometric series question

• mpx86
In summary, the expression 2^32 – {(2 + 1) (2^2 + 1) (2^4+1) (2^8+1) (2^16+1)} is equal to 1. However, the options provided do not match this result due to an error in the question statement. The correct solution was found by using the iteration (1+x) (1+x^2) = (x^4-1)/x-1.
mpx86

## Homework Statement

2^32 – (2 + 1) (2^2 – 1) (2^4+1) (2^8+1) (2^16+1)} is equal to

## The Attempt at a Solution

Solved it by opening the bracket
Answer: 2^31 + 2^24 + 2^ 18 - 2^7 + 2
Option' are
0
1
2
2^16

None of the options matched... Is there a mistake in question statement or my solution of the same?[/B]

mpx86 said:

## Homework Statement

2^32 – (2 + 1) (2^2 – 1) (2^4+1) (2^8+1) (2^16+1)} is equal to

## The Attempt at a Solution

Solved it by opening the bracket
Answer: 2^31 + 2^24 + 2^ 18 - 2^7 + 2
Option' are
0
1
2
2^16

None of the options matched... Is there a mistake in question statement or my solution of the same?[/B]

lol solved... there was an error in question statement:
question was 2^32 – {(2 + 1) (2^2 + 1) (2^4+1) (2^8+1) (2^16+1)}
(1+x) (1+x^2) = (x^4-1)/x-1
using this iteration yields answer as 1
thanks anyways :)

## 1. What is a geometric series?

A geometric series is a sequence of numbers where each term is found by multiplying the previous term by a constant value called the common ratio. The general form of a geometric series is a + ar + ar^2 + ar^3 + ..., where a is the first term and r is the common ratio.

## 2. How do you find the sum of a geometric series?

The sum of a finite geometric series can be found using the formula S = a(1-r^n)/(1-r), where S is the sum, a is the first term, r is the common ratio, and n is the number of terms. For an infinite geometric series, the sum can be found using the formula S = a/(1-r), as long as the absolute value of the common ratio is less than 1.

## 3. What is the common ratio in a geometric series?

The common ratio in a geometric series is the number by which each term is multiplied to get the next term. It is usually represented by the variable r and is calculated by dividing any term by the previous term.

## 4. How do you determine if a series is geometric?

A series is geometric if each term is found by multiplying the previous term by the common ratio. You can also check for a constant ratio between consecutive terms to determine if a series is geometric.

## 5. What real-life applications use geometric series?

Geometric series have many real-life applications, such as calculating compound interest in financial investments, modeling population growth, and in physics to describe the decay of radioactive materials. They are also commonly used in computer science, engineering, and statistics.

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