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Properties of Iota

If n 2 +n=6...

Question

If $n^{2} + n = 6$ , then find the value of $n$ .

A

n = 2, 3

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B

n = - 2, - 3

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C

n = 2, - 3

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D

n = - 2, 3

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Solution

The correct option is C $n = 2, - 3$
$\Rightarrow n^{2} + n - 6 = 0$
$\Rightarrow (n + 3) (n - 2) = 0$
$\Rightarrow n = 2 o r n = - 3$

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n

is a positive integer, then find the value of

⎡ ⎢ ⎣ \begin{matrix} ^{n + 2} C_{n} & ^{n + 3} C_{n + 1} & ^{n + 4} C_{n + 2}^{n + 3} C_{n + 1} & ^{n + 4} C_{n + 2} & ^{n + 5} C_{n + 3}^{n + 4} C_{n + 2} & ^{n + 5} C_{n + 3} & ^{n + 6} C_{n + 4} \end{matrix} ⎤ ⎥ ⎦

n^{2} + n = 2

, then find the value of

n .

n^{2} = (n + 6)

, then find the value of

n .

Q. The value of

n l i m - - \to \infty \frac{1. n + 2. (n - 1) + 3. (n - 2) + . . . + n .1}{1^{2} + 2^{2} + . . . + n^{2}}

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^{n} C_{0} -^{n} C_{1} 3^{1} +^{n} C_{2} 3^{2} + \dots + (- 1)^{n}^{n} c_{n} 3^{n}

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