Expression explicite d'une suite et calculs de ses premiers termes

Exercice 1

Soit

n

un entier naturel.
Calculer les trois premiers termes de chacune des suites suivantes :

$u_{n} =2n^{2} -3n-5$

Correction

$u_{n} =\frac{n-5}{2n+4}$

Correction

$u_{n} =\frac{2^{n} }{n+3}$

Correction

$u_{n} =\sqrt{2n+5}$

Correction

Exercice 2

Soit

n

un entier naturel.
Calculer les trois premiers termes de chacune des suites suivantes :

$u_{n} =5n^{2} -7n-3$

Correction

$u_{n} =\frac{-6+2n}{5n+3}$

Correction

$u_{n} =\frac{3^{n+1} }{n+9}$

Correction

$u_{n} =\sqrt{4^{n}+2n}$

Correction

Exercice 3

Soit

n

un entier naturel.
Calculer les trois premiers termes de chacune des suites suivantes :

$u_{n} =\frac{1}{3}n^{2} -6n+1$

Correction

$u_{n} =\frac{n+6}{4n-8}$

Correction

$u_{n} =\frac{5n-2}{4^{n}}$

Correction

$u_{n} =\frac{1}{4}\sqrt{n+7}$

Correction

Exercice 1

un=2n2−3n−5u_{n} =2n^{2} -3n-5un​=2n2−3n−5

un=n−52n+4u_{n} =\frac{n-5}{2n+4} un​=2n+4n−5​

un=2nn+3u_{n} =\frac{2^{n} }{n+3}un​=n+32n​

un=2n+5u_{n} =\sqrt{2n+5}un​=2n+5​

Exercice 2

un=5n2−7n−3u_{n} =5n^{2} -7n-3un​=5n2−7n−3

un=−6+2n5n+3u_{n} =\frac{-6+2n}{5n+3} un​=5n+3−6+2n​

un=3n+1n+9u_{n} =\frac{3^{n+1} }{n+9}un​=n+93n+1​

un=4n+2nu_{n} =\sqrt{4^{n}+2n}un​=4n+2n​

Exercice 3

un=13n2−6n+1u_{n} =\frac{1}{3}n^{2} -6n+1un​=31​n2−6n+1

un=n+64n−8u_{n} =\frac{n+6}{4n-8} un​=4n−8n+6​

un=5n−24nu_{n} =\frac{5n-2}{4^{n}}un​=4n5n−2​

un=14n+7u_{n} =\frac{1}{4}\sqrt{n+7}un​=41​n+7​

$u_{n} =2n^{2} -3n-5$

$u_{n} =\frac{n-5}{2n+4}$

$u_{n} =\frac{2^{n} }{n+3}$

$u_{n} =\sqrt{2n+5}$

$u_{n} =5n^{2} -7n-3$

$u_{n} =\frac{-6+2n}{5n+3}$

$u_{n} =\frac{3^{n+1} }{n+9}$

$u_{n} =\sqrt{4^{n}+2n}$

$u_{n} =\frac{1}{3}n^{2} -6n+1$

$u_{n} =\frac{n+6}{4n-8}$

$u_{n} =\frac{5n-2}{4^{n}}$

$u_{n} =\frac{1}{4}\sqrt{n+7}$