Evaluate -n-1N Un if Un- - n 1 5- n2 2N-1 2N-1- n3 3N2 3N- - -

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Properties of Determinants

Evaluate ∑n...

Question

Evaluate $N \sum n = 1 U_{n}$ if
$U_{n} =$ $∣ ∣ ∣ ∣ ∣ \begin{matrix} n & 1 & 5 n^{2} & 2 N + 1 & 2 N + 1 n^{3} & 3 N^{2} & 3 N \end{matrix} ∣ ∣ ∣ ∣ ∣$

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U_{n} = \frac{n!}{(n + 2)!}

n \in N .

S_{n} = \sum_{n - 1}^{n} U_{n}

{lim}_{n \to \infty} S_{n}

If U_{n} = ⎛ ⎜ ⎝ \begin{matrix} n & 1 & 5 n^{2} & 2 N + 1 & 2 N + 1 n^{3} & 3 N^{2} & 3 N \end{matrix} ∣ ∣ ∣ ∣ ∣, then N \sum U_{n} = n = 1

If U_{n} = ⎛ ⎜ ⎝ \begin{matrix} n & 1 & 5 n^{2} & 2 N + 1 & 2 N + 1 n^{3} & 3 N^{2} & 3 N \end{matrix} ∣ ∣ ∣ ∣ ∣, then N \sum U_{n} = n = 1

f (x) = \frac{a^{x}}{a^{x} + \sqrt{a}} (a > 0)

2 n - 1 \sum r = 1 2 f (\frac{r}{2 n})

50 \sum n = 1 (2^{n} - 1)

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