Binomial Theorem: 11 Terms Explained

Ananya0107 · 2015-03-25T11:03:19+00:00

Any hints for this : 1- (11C1/2.3 ).2^2 + (11C2/3.4 ). 2^3 ...so on up to 12 terms .

Thread starter Ananya0107
Start date Mar 25, 2015
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Binomial Binomial theorem Theorem

In summary, the Binomial Theorem is a mathematical formula that calculates the expansion of expressions with two terms raised to a power. It has 11 terms and is used to simplify complex calculations and find specific coefficients and terms. The general form is (a + b)^n = Σ (nCr)(a^(n-r))(b^r), and it has applications in statistics, physics, and engineering. Common mistakes include forgetting terms, using incorrect coefficients or powers, and not using proper notation.

Mar 25, 2015

Ananya0107

Any hints for this
: 1- (11_C₁/2.3 ).2^2 + (11_C₂/3.4 ). 2^3 ...so on up to 12 terms .

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Mar 25, 2015

Ananya0107

We have to find the sum...

Mar 25, 2015

Mentallic

Homework Helper

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[tex](1-x)^n[/tex] and consider this expansion when x=2 and n=11. Now take the integral of the expansion, do you see a pattern emerging? Can you take it from there?

Mar 25, 2015

Ananya0107

Yes, thanks

Related to Binomial Theorem: 11 Terms Explained

1. What is the Binomial Theorem and why is it important?

The Binomial Theorem is a mathematical formula that allows us to expand expressions with two terms raised to a power. It is important because it simplifies complex calculations and allows us to find specific coefficients and terms in a binomial expansion.

2. How many terms are there in the Binomial Theorem?

There are 11 terms in the Binomial Theorem, which is why it is sometimes referred to as the "11-term Binomial Theorem". These terms represent the coefficients of each term in a binomial expansion.

3. What is the general form of the Binomial Theorem?

The general form of the Binomial Theorem is (a + b)^n = Σ (nCr)(a^(n-r))(b^r), where a and b are the two terms, n is the power, nCr represents the combination of n and r, and r represents the power of b in each term.

4. How is the Binomial Theorem used in real-life applications?

The Binomial Theorem has various applications in fields such as statistics, physics, and engineering. It is used to solve problems related to combinations, probability, and binomial distributions. It is also used to expand equations in physics and engineering calculations.

5. What are some common mistakes to avoid when using the Binomial Theorem?

One common mistake is forgetting to include all 11 terms in the expansion. Another mistake is using incorrect coefficients or powers for each term. It is also important to be careful with negative powers and to use proper notation when writing out the expanded form.