Question

Vă rog !!! Dau coroana !!!​

Answer 1

Explicație pas cu pas:

a)

$a_{n} = - n(n+2), \ \ n \geqslant 1$

$n = 1 \implies a_{1} = - 1\cdot (1+2) \iff a_{1} = - 1\cdot 3 = - 3 \\ n = 2 \implies a_{2} = - 2\cdot (2+2) \iff a_{1} = - 2\cdot 4 = - 6 \\ n = 3 \implies a_{3} = - 3\cdot (3+2) \iff a_{1} = - 3\cdot 5 = - 15$

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b)

$b_{n} = \sqrt{n} - \sqrt{n - 1}$

condiții de existență:

$n \geqslant 0 \ \ si \ \ n - 1 \geqslant 0 \implies n \geqslant 1$

$n = 1 \implies b_{1} = \sqrt{1} - \sqrt{1 - 1} \iff b_{1} = 1 - \sqrt{0}$

$\bf b_{1} = 1$

$n = 2 \implies b_{2} = \sqrt{2} - \sqrt{2 - 1} \iff b_{2} = \sqrt{2} - \sqrt{1}$

$\bf b_{2} = \sqrt{2} - 1$

$n = 3 \implies b_{3} = \sqrt{3} - \sqrt{3 - 1}$

$\bf b_{3} = \sqrt{3} - \sqrt{2}$

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