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AllQuestion and Answers: Page 108

Question Number 206396 Answers: 3 Comments: 0

Question Number 206394 Answers: 0 Comments: 1

Question Number 206393 Answers: 1 Comments: 0

find S=1+Σ_ℓ (((−)^ℓ )/ℓ)((1/ℓ)−(1/(ℓ+1))) , ℓ∈[1,∞) 1+Σ_ℓ (((−)^ℓ )/ℓ)((1/ℓ)−(1/(ℓ+1))) 1−(1−(1/2))+(1/2)((1/2)−(1/3))−(1/3)((1/3)−(1/4))+(1/4)((1/4)−(1/5))−......

$find S = 1 + \sum_{ℓ} \frac{{(-)}^{ℓ}}{ℓ} (\frac{1}{ℓ} - \frac{1}{ℓ + 1}), ℓ \in [1, \infty)$ $1 + \sum_{ℓ} \frac{{(-)}^{ℓ}}{ℓ} (\frac{1}{ℓ} - \frac{1}{ℓ + 1})$ $1 - (1 - \frac{1}{2}) + \frac{1}{2} (\frac{1}{2} - \frac{1}{3}) - \frac{1}{3} (\frac{1}{3} - \frac{1}{4}) + \frac{1}{4} (\frac{1}{4} - \frac{1}{5}) - . . . . . .$

Question Number 206391 Answers: 2 Comments: 0

Find: ∫_(−3) ^( −2) (∣x∣ + ∣x − 4∣) dx = ?

$Find :$ $\int_{- 3}^{- 2} (∣ x ∣ + ∣ x - 4 ∣) dx = ?$

Question Number 206365 Answers: 2 Comments: 4

Number series: a_3 = 2a + b − 6 a_9 = a + b + 5 a_(15) = 3a + b − 7 Find: a = ?

$Number series :$ $a_{3} = 2 a + b - 6$ $a_{9} = a + b + 5$ $a_{15} = 3 a + b - 7$ $Find : a = ?$

Question Number 206364 Answers: 2 Comments: 0

Question Number 206363 Answers: 0 Comments: 2

If 0<a<1 Compare: (1/(a−1)) , (a/(a−1)) , (1/(1−a)) , (a/(1−a)) , (a/(2a))

$If 0 < a < 1$ $Compare :$ $\frac{1}{a - 1}, \frac{a}{a - 1}, \frac{1}{1 - a}, \frac{a}{1 - a}, \frac{a}{2 a}$

Question Number 206357 Answers: 2 Comments: 0

Find: 1 + cos444° − cos84° + cot45° = ?

$Find :$ $1 + \cos 444 ° - \cos 84 ° + \cot 45 ° = ?$

Question Number 206355 Answers: 2 Comments: 0

if the sum of three positive real numbers is equal to their product, prove that at least one of the numbers is larger than 1.7.

$i f t h e s u m o f t h r e e p o s i t i v e r e a l$ $n u m b e r s i s e q u a l t o t h e i r p r o d u c t,$ $p r o v e t h a t a t l e a s t o n e o f t h e$ $n u m b e r s i s l a r g e r t h a n 1.7 .$

Question Number 206353 Answers: 0 Comments: 6

Question Number 206351 Answers: 0 Comments: 1

expression of the sequence (a_n ) defined by { ((a_0 >0 , a_1 >0)),((a_(n+2) =((2(−1)^n )/(n+2))−((2(−1)^n (2n+3))/(n+2))a_(n+1) +((n+1)/(n+2))a_n )) :}

$e x p r e s s i o n o f t h e s e q u e n c e (a_{n}) d e f i n e d$ $b y$ ${\begin{cases} a_{0} > 0, a_{1} > 0 \\ a_{n + 2} = \frac{2 {(- 1)}^{n}}{n + 2} - \frac{2 {(- 1)}^{n} (2 n + 3)}{n + 2} a_{n + 1} + \frac{n + 1}{n + 2} a_{n} \end{cases}$

Question Number 206340 Answers: 2 Comments: 0

∫_0 ^( 1) (( ln(1−x )ln(1+x ))/x)dx = Σ_(n=1) ^∞ Ω_n find : Σ_(n=1) ^∞ n Ω_n = ?

$\int_{0}^{1} \frac{l n (1 - x) l n (1 + x)}{x} d x = \underset{n = 1}{\sum^{\infty}} Ω_{n}$ $f i n d : \underset{n = 1}{\sum^{\infty}} n Ω_{n} = ?$

Question Number 206339 Answers: 1 Comments: 0

E ⊆ Y ⊆ ( X , d )∣_(metric space) prove E is open in Y if and only if ∃ G (open set ) in X such that E = G ∩ Y .... (mathematical analysis (I))

$E \subseteq Y \subseteq (X, d) ∣_{m e t r i c s p a c e}$ $p r o v e E i s o p e n i n Y i f a n d o n l y i f$ $\exists G (o p e n s e t) i n X s u c h t h a t$ $E = G \cap Y . . . . (m a t h e m a t i c a l a n a l y s i s (I))$

Question Number 206338 Answers: 1 Comments: 0

Question Number 206367 Answers: 4 Comments: 2

Find: (1/6) + (1/(24)) + (1/(60)) + ... + ... (1/(720)) = ?

$Find :$ $\frac{1}{6} + \frac{1}{24} + \frac{1}{60} + . . . + . . . \frac{1}{720} = ?$

Question Number 206332 Answers: 1 Comments: 0

If log(a + b + c) = loga + logb + logc then prove that log(((2a)/(1 − a^2 )) + ((2b)/(1 − b^2 )) + ((2c)/(1 − c^2 ))) = log(((2a)/(1 − a^2 ))) + log(((2b)/(1 − b^2 ))) + log(((2c)/(1 − c^2 ))).

$If \log (a + b + c) = \log a + \log b + \log c$ $then prove that$ $\log (\frac{2 a}{1 - a^{2}} + \frac{2 b}{1 - b^{2}} + \frac{2 c}{1 - c^{2}}) =$ $\log (\frac{2 a}{1 - a^{2}}) + \log (\frac{2 b}{1 - b^{2}}) + \log (\frac{2 c}{1 - c^{2}}) .$

Question Number 206328 Answers: 2 Comments: 0

f(x)= ⌊ (( 1+ x +x^2 )/(x+ x^( 2) )) ⌋ is given. ⇒ { (( D_f = ? (domain ))),(( R_( f) = ?( range))) :}

$f (x) = ⌊ \frac{1 + x + x^{2}}{x + x^{2}} ⌋ i s g i v e n .$ $\Rightarrow {\begin{cases} D_{f} = ? (d o m a i n) \\ R_{f} = ? (r a n g e) \end{cases}$

Question Number 206323 Answers: 0 Comments: 0

Question Number 206322 Answers: 1 Comments: 1

If abc = 1 then prove that (1/(1 + a + b^(−1) )) + (1/(1 + b + c^(−1) )) + (1/(1 + c + a^(−1) )) = 1

$If a b c = 1 then prove that$ $\frac{1}{1 + a + b^{- 1}} + \frac{1}{1 + b + c^{- 1}} + \frac{1}{1 + c + a^{- 1}} = 1$

Question Number 206321 Answers: 2 Comments: 0

Question Number 206319 Answers: 0 Comments: 0

Question Number 206318 Answers: 0 Comments: 0

∫_0 ^1 ∫_0 ^1 ((xln(1+y)ln(1−x))/(1+x^2 y))dxdy

$\int_{0}^{1} \int_{0}^{1} \frac{x l n (1 + y) l n (1 - x)}{1 + x^{2} y} d x d y$

Question Number 206362 Answers: 2 Comments: 0

sin(π/7) × sin((2π)/7) × sin((3π)/7) = ?

$\sin \frac{π}{7} \times \sin \frac{2 π}{7} \times \sin \frac{3 π}{7} = ?$

Question Number 206311 Answers: 0 Comments: 0

Hi everyone... This is not a question per say (sorry ′bout that). It′s just that for past 4 years, to type math messages to my friends (text messages) I′ve been painfully using the two most famous android ones (matheditor and dxmath). And I was thinking, I realised how typing on this app on android (matheditor) is so much more practical. So if any one here knows how to code, I would love to see an android−keyboard adaptation (only with the unicode charters on this keyboard that is... and with the extra ^(1234567890−+×()inx) _(1234567890inx) unicode ones that might come in handy once we can′t use proper indexation) I would personnaly be ready to pay for it. And I would be intersted to know if anyone of you would be too. I don′t think it would be very hard to do... I am ready to help if I can. I don′t know how to make an android app, but being a mathematician and a physicist, I′m sure I can make myself usefull...

$Hi everyone . . .$ $This is not a question per say (sorry^{'} bout$ $that) . {It}^{'} s just that for past 4 years, to type$ $math messages to my friends (text messages)$ $I^{'} ve been painfully using the two most famous$ $android ones (m a t h e d i t o r and d x m a t h) .$ $And I was thinking, I realised how typing$ $on this app on android (m a t h e d i t o r) is so$ $much more practical .$ $So if any one here knows how to code, I would$ $love to see an android - keyboard adaptation$ $(only with the unicode charters on this$ $keyboard that is . . . and with the extra$ $^{1234567890 - + \times () inx}_{1234567890 inx} unicode ones$ $that might come in handy once we {can}^{'} t use$ $proper indexation)$ $I would personnaly be ready to pay for it .$ $And I would be intersted to know if anyone$ $of you would be too .$ $I {don}^{'} t think it would be very hard to do . . .$ $I am ready to help if I can . I {don}^{'} t know how$ $to make an android app, but being a$ $mathematician and a physicist, I^{'} m sure$ $I can make myself usefull . . .$

Question Number 206309 Answers: 2 Comments: 0

Find the ways to express 11025 as product of two factors. (a) 13 (b) 14 (c) 26 (d) 27

$Find the ways to express 11025$ $as product of two factors .$ $(a) 13 (b) 14 (c) 26 (d) 27$

Question Number 206303 Answers: 1 Comments: 0

log_2 4

${l o g}_{2} 4$

Pg 103 Pg 104 Pg 105 Pg 106 Pg 107 Pg 108 Pg 109 Pg 110 Pg 111 Pg 112

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