Binomial Theorem Maths Binomial Theorem Maths Class 11th

For integers n and r, let

The maximum value of k for which the sum

$\sum_{i = 0}^{k} (\begin{matrix} 10 & i \end{matrix}) (\begin{matrix} 15 & k - i \end{matrix}) + \sum_{i = 0}^{k + 1} (\begin{matrix} 12 & i \end{matrix}) (\begin{matrix} 13 & k + 1 - i \end{matrix})$

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

$\sum_{i = 0}^{k} (\begin{array}{l} 10 \\ i \end{array}) (\begin{array}{l} 15 \\ K - i \end{array}) + \sum_{i = 0}^{k + 1} (\begin{array}{l} 12 \\ i \end{array}) (\begin{array}{l} 13 \\ k + 1 - i \end{array})$

= Equating the coefficient of $x^{k} i n {(1 + x)}^{25} =^{25} C_{k}$ .(i)

= Equating the coefficient of $x^{k + 1} i n {(1 + x)}^{12} {(x + 1)}^{13}$

From (i) and (ii)

Hence $26 \geq k + 1 \Rightarrow k \leq 25$

But maximum value of k is not defined bonus

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Similar Questions for you

Kindly consider the following

alok kumar singh

${(1 + x)}^{11} =^{11} C_{0} +^{11} C_{1} x +^{11} C_{2} x^{2} + . . . . . +^{11} C_{11} x^{11}$

= \frac{2^{12} - 2 - 24}{12}

= \frac{2^{12} - 26}{12} = \frac{4070}{12} = \frac{2035}{6} = \frac{m}{n}

m + n = 2035 + 6 = 2041

Number of integral terms in the binomial expansion of (7^1/2 + 11^1/6)⁸²⁴ is

alok kumar singh

$T_{n + 1} =^{n} C_{r} 1 1^{\frac{1}{6}} \cdot 7^{\frac{824 - 4}{2}}$

For integral term

6 should divide r

and $\frac{824 - r}{2}$ must be integer

->2 most divide r

->r divisible by 6

->possible values of r Î {0, 1, 2, …824}

->For integer terms

r Î {0, 6, 12, …822} (822 = 0 + (n – 1)6 Þ n = 138)

= 138 terms

Which are the common mistakes by students in binomial theorem class 11?

Pallavi Pathak

The common mistakes can be - using the formula incorrectly, before applying the formula students not simplify the expression, in Binomial Expansion, sometimes they forget to include the fractional and negative exponents, and using incorrect values for a, b, and n.

Which is the another name of the binomial model.

Pallavi Pathak

The Binomial model is known as the Lattice Model or Binomial Option Pricing Model.

What is the total number of exercises in binomial theorem class 11?

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There are a total of 36 questions comprising 14 straightforward formula-based sums, 16 challenging problems, and 6 intermediate.

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For integers n and r, let

The maximum value of k for which the sum

$\sum_{i = 0}^{k} (\begin{matrix} 10 & i \end{matrix}) (\begin{matrix} 15 & k - i \end{matrix}) + \sum_{i = 0}^{k + 1} (\begin{matrix} 12 & i \end{matrix}) (\begin{matrix} 13 & k + 1 - i \end{matrix})$

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For integers n and r, let The maximum value of k for which the sum ∑ i = 0 k ( 1 0 i ) ( 1 5 k − i ) + ∑ i = 0 k + 1 ( 1 2 i ) ( 1 3 k + 1 − i )

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For integers n and r, let

The maximum value of k for which the sum

$\sum_{i = 0}^{k} (\begin{matrix} 10 & i \end{matrix}) (\begin{matrix} 15 & k - i \end{matrix}) + \sum_{i = 0}^{k + 1} (\begin{matrix} 12 & i \end{matrix}) (\begin{matrix} 13 & k + 1 - i \end{matrix})$