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Question Number 32037 Answers: 0 Comments: 1

let u_n =cos(π(√(n^2 +n+1))) find nature of Σ u_n .

$l e t u_{n} = c o s (π \sqrt{n^{2} + n + 1}) f i n d n a t u r e o f Σ u_{n} .$

Question Number 32036 Answers: 0 Comments: 0

nature of Σ u_n with u_n = (1/((ln(2))^2 +....+(ln(n))^2 )) .

$n a t u r e o f Σ u_{n} w i t h u_{n} = \frac{1}{{(l n (2))}^{2} + . . . . + {(l n (n))}^{2}} .$

Question Number 32034 Answers: 0 Comments: 0

let u_n = ∫_0 ^1 (dx/(1+x+...+x^n )) study the convergence of Σ u_n .

$l e t u_{n} = \int_{0}^{1} \frac{d x}{1 + x + . . . + x^{n}} s t u d y t h e c o n v e r g e n c e o f$ $Σ u_{n} .$

Question Number 32033 Answers: 0 Comments: 0

let consider the sequence (u_n ) /u_0 ∈[0,1] and ∀n∈N u_(n+1) = u_n −u_n ^2 1) give a simple equivalent of u_n 2) find the nature of Σ u_n .

$l e t c o n s i d e r t h e s e q u e n c e (u_{n}) / u_{0} \in [0, 1] a n d$ $\forall n \in N u_{n + 1} = u_{n} - u_{n}^{2}$ $1) g i v e a s i m p l e e q u i v a l e n t o f u_{n}$ $2) f i n d t h e n a t u r e o f Σ u_{n} .$

Question Number 32031 Answers: 0 Comments: 1

let f(a) = ∫_0 ^∞ e^(−ax) ln(x)dx with a>0 1) find f(a) 2) find ∫_0 ^∞ e^(−ax) (xlnx)dx 3) calculate ∫_0 ^∞ e^(−2x) (xlnx)dx .

$l e t f (a) = \int_{0}^{\infty} e^{- a x} l n (x) d x w i t h a > 0$ $1) f i n d f (a)$ $2) f i n d \int_{0}^{\infty} e^{- a x} (x l n x) d x$ $3) c a l c u l a t e \int_{0}^{\infty} e^{- 2 x} (x l n x) d x .$

Question Number 32029 Answers: 0 Comments: 0

calculate ∫_0 ^∞ e^(−αx) ln(x) dx with α>0 .

$c a l c u l a t e \int_{0}^{\infty} e^{- α x} l n (x) d x w i t h α > 0 .$

Question Number 32028 Answers: 1 Comments: 0

If ((2z_1 )/(3z_2 )) is a purely imaginary number, then find the value of ∣((z_1 −z_2 )/(z_1 +z_2 ))∣ .

$I f \frac{2 z_{1}}{3 z_{2}} i s a p u r e l y i m a g i n a r y n u m b e r,$ $t h e n f i n d t h e v a l u e o f ∣ \frac{z_{1} - z_{2}}{z_{1} + z_{2}} ∣ .$

Question Number 32026 Answers: 0 Comments: 1

let α>0 prove that Σ_(n=0) ^∞ (((−1)^n )/(n+α)) =∫_0 ^1 (x^(α−1) /(1+x))dx .

$l e t α > 0 p r o v e t h a t \sum_{n = 0}^{\infty} \frac{{(- 1)}^{n}}{n + α} = \int_{0}^{1} \frac{x^{α - 1}}{1 + x} d x .$

Question Number 32025 Answers: 0 Comments: 2

calculate Σ_(n=0) ^∞ (((−1)^n )/(4n+1)) .

$c a l c u l a t e \sum_{n = 0}^{\infty} \frac{{(- 1)}^{n}}{4 n + 1} .$

Question Number 32008 Answers: 1 Comments: 3

lim_(n→∞) [((1/n))^n +((2/n))^n +..+((n/n))^n ]=...

$\lim_{n \to \infty} [{(\frac{1}{n})}^{n} + {(\frac{2}{n})}^{n} + . . + {(\frac{n}{n})}^{n}] = . . .$

Question Number 32002 Answers: 1 Comments: 0

If z^3 =z^ prove then ∣z∣=1.

$I f z^{3} = \bar{z} p r o v e$ $t h e n ∣ z ∣= 1 .$

Question Number 31991 Answers: 0 Comments: 1

g_n =(√(g_(n−1) +g_(n−2) )) g_1 =1 g_2 =3 g_n =..

$g_{n} = \sqrt{g_{n - 1} + g_{n - 2}}$ $g_{1} = 1$ $g_{2} = 3$ $g_{n} = . .$

Question Number 31990 Answers: 1 Comments: 3

a_n =2a_(n−1) +3a_(n−2) a_0 =1 a_1 =2 a_n =...

$a_{n} = 2 a_{n - 1} + 3 a_{n - 2}$ $a_{0} = 1$ $a_{1} = 2$ $a_{n} = . . .$

Question Number 31984 Answers: 0 Comments: 1

study the covergence of Σ u_n with u_n =^n (√(n/(n+1))) −1 .

$s t u d y t h e c o v e r g e n c e o f Σ u_{n} w i t h$ $u_{n} =^{n} \sqrt{\frac{n}{n + 1}} - 1 .$

Question Number 31983 Answers: 0 Comments: 2

calculate Σ_(n=0) ^∞ ((n^2 −2)/(n!)) .

$c a l c u l a t e \sum_{n = 0}^{\infty} \frac{n^{2} - 2}{n!} .$

Question Number 31982 Answers: 0 Comments: 2

find the value of Σ_(n=0) ^∞ (((−1)^n )/((2n+1)(2n+3))) .

$f i n d t h e v a l u e o f \sum_{n = 0}^{\infty} \frac{{(- 1)}^{n}}{(2 n + 1) (2 n + 3)} .$

Question Number 31981 Answers: 0 Comments: 1

find the nature of Σ_(n≥2) (1/(nln(n))) .

$f i n d t h e n a t u r e o f \sum_{n ⩾ 2} \frac{1}{n l n (n)} .$

Question Number 31980 Answers: 0 Comments: 0

let −1<x<1 calculate Σ_(n=1) ^∞ (x^n /((1−x^n )(1−x^(n+1) ))) .

$l e t - 1 < x < 1 c a l c u l a t e \sum_{n = 1}^{\infty} \frac{x^{n}}{(1 - x^{n}) (1 - x^{n + 1})} .$

Question Number 31979 Answers: 0 Comments: 1

calculate Σ_(n=2) ^∞ (1/((n^2 −1)^2 )) .

$c a l c u l a t e \sum_{n = 2}^{\infty} \frac{1}{{(n^{2} - 1)}^{2}} .$

Question Number 31978 Answers: 1 Comments: 0

find the value of Σ_(n=0) ^∞ (1/((2n+1)(2n+3)(2n+5))).

$f i n d t h e v a l u e o f \sum_{n = 0}^{\infty} \frac{1}{(2 n + 1) (2 n + 3) (2 n + 5)} .$

Question Number 31977 Answers: 1 Comments: 2

find the value of Σ_(n=0) ^∞ (1/((2n+1)(2n+3)))

$f i n d t h e v a l u e o f \sum_{n = 0}^{\infty} \frac{1}{(2 n + 1) (2 n + 3)}$

Question Number 31976 Answers: 0 Comments: 0

let u_n =^(n+1) (√(n+1)) −^n (√n) find radius of convergence for Σ u_n z^n (z∈C).

$l e t u_{n} =^{n + 1} \sqrt{n + 1} -^{n} \sqrt{n} f i n d r a d i u s o f c o n v e r g e n c e$ $f o r Σ u_{n} z^{n} (z \in C) .$

Question Number 31975 Answers: 0 Comments: 0

let u_n = ∫_1 ^∞ e^(−t^n ) dt 1) calculate lim_(n→∞) u_n 2)find a equivalent of u_n (n→∞) 3)find the radius of convergence of Σ u_n x^n .

$l e t u_{n} = \int_{1}^{\infty} e^{- t^{n}} d t$ $1) c a l c u l a t e {l i m}_{n \to \infty} u_{n}$ $2) f i n d a e q u i v a l e n t o f u_{n} (n \to \infty)$ $3) f i n d t h e r a d i u s o f c o n v e r g e n c e o f Σ u_{n} x^{n} .$

Question Number 31974 Answers: 0 Comments: 0

1)find I(p,q) = ∫_0 ^1 t^p (1−t)^q dt with pand q integrs 2) find the nature of Σ I_((n,n))

$1) f i n d I (p, q) = \int_{0}^{1} t^{p} {(1 - t)}^{q} d t w i t h p a n d q i n t e g r s$ $2) f i n d t h e n a t u r e o f Σ I_{(n, n)}$

Question Number 31973 Answers: 0 Comments: 0

let give the sequence (u_n ) / u_0 =1 and u_1 =−1 and u_(n+2) = 2u_(n+1 ) −u_n .find the radius of convegence for this serie.

$l e t g i v e t h e s e q u e n c e (u_{n}) / u_{0} = 1 a n d u_{1} = - 1 a n d$ $u_{n + 2} = 2 u_{n + 1} - u_{n} . f i n d t h e r a d i u s o f c o n v e g e n c e f o r$ $t h i s s e r i e .$

Question Number 31972 Answers: 0 Comments: 1

solve inside ]−1,1[ the d.e. (√(1−x^2 )) y^′ +y =e^(−2x) .

$s o l v e i n s i d e] - 1, 1 [t h e d . e . \sqrt{1 - x^{2}} y^{^{'}} + y = e^{- 2 x} .$

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