If x2r occurs in x- 2 x 2 n- then n-2r must be of the form

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General Term of Binomial Expansion

If x2r occu...

Question

If $x^{2 r}$ occurs in ${(x + \frac{2}{x^{2}})}^{n}$ , then $n - 2 r$ must be of the form

3 k

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3 k - 1

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3 k + 1

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4 k \pm 1

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(k - 1) x + (3 k + 1) y + 2 k z = 0 (k - 1) x + (4 k - 2) y + (k + 3) z = 0 2 x + (3 k + 1) y + 3 (k - 1) z = 0

k = 0, 3

f

N \to N

f (n) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 2, n = 3 k, & k \in Z 10 - n, n = 3 k + 1, & k \in Z 0, n = 3 k + 2, & k \in Z \end{matrix}

{n \in N : f (n) > 2} =

k

\frac{1}{3} k + \frac{1}{4} k = 1

x^{2 r}

{(x + \frac{1}{x^{2}})}^{n - 3}

(\frac{n - 2 r}{3})

The square of a positive integer cannot be of the form of (K is some integer)

A}3k+1. B}4k+2 C}5k+1. D}5k+4

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