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Question Number 111769 Answers: 0 Comments: 0

let u_n =Σ_(k=1) ^n (1/(√((k+n)(k+n+1)))) detremine lim_(n→+∞) u_n

$let u_{n} = \sum_{k = 1}^{n} \frac{1}{\sqrt{(k + n) (k + n + 1)}}$ $detremine \lim_{n \to + \infty} u_{n}$

Question Number 111768 Answers: 0 Comments: 0

explicite f(x) =∫_0 ^(2π) ln(x^2 −2xcosθ +1)dθ (x≠+^− 1)

$explicite f (x) = \int_{0}^{2 π} \ln (x^{2} - 2 xcos θ + 1) d θ (x \neq \bar{+} 1)$

Question Number 111766 Answers: 2 Comments: 0

calculate lim_(n→+∞) Σ_(k=1) ^n ln((n/(n+k)))^(1/n)

$calculate \lim_{n \to + \infty} \sum_{k = 1}^{n} \ln {(\frac{n}{n + k})}^{\frac{1}{n}}$

Question Number 111762 Answers: 1 Comments: 0

caoculate ∫_0 ^(π/4) ln(1+2tanx)dx

$caoculate \int_{0}^{\frac{π}{4}} \ln (1 + 2 tanx) dx$

Question Number 111760 Answers: 0 Comments: 0

find lim_(x→1^+ ) ∫_x ^x^2 ((ln(t))/((t−1)^2 ))dx

$find \lim_{x \to 1^{+}} \int_{x}^{x^{2}} \frac{\ln (t)}{{(t - 1)}^{2}} dx$

Question Number 111756 Answers: 0 Comments: 0

find I_n =∫_0 ^(π/4) (du/(cos^n u))

$find I_{n} = \int_{0}^{\frac{π}{4}} \frac{du}{\cos^{n} u}$

Question Number 111755 Answers: 2 Comments: 0

calculate lim_(n→+∞) Σ_(k=1) ^n (√((n−k)/(n^3 +n^2 k)))

$calculate \lim_{n \to + \infty} \sum_{k = 1}^{n} \sqrt{\frac{n - k}{n^{3} + n^{2} k}}$

Question Number 111754 Answers: 2 Comments: 0

calculate lim_(n→+∞) Σ_(k=1) ^(2n) (k/(k^2 +n^2 ))

$calculate \lim_{n \to + \infty} \sum_{k = 1}^{2 n} \frac{k}{k^{2} + n^{2}}$

Question Number 111887 Answers: 0 Comments: 0

Question Number 111882 Answers: 1 Comments: 0

(√(bemath)) (1)lim_(x→∞) [(x^2 /(x+1)) − (x^2 /(x+3)) ] ? (2) prove that n^2 ≤ 2^n for ∀n∈N by mathematical induction

$\sqrt{b e m a t h}$ $(1) \lim_{x \to \infty} [\frac{x^{2}}{x + 1} - \frac{x^{2}}{x + 3}] ?$ $(2) p r o v e t h a t n^{2} ⩽ 2^{n} f o r \forall n \in N$ $b y m a t h e m a t i c a l i n d u c t i o n$

Question Number 111745 Answers: 0 Comments: 6

Question Number 111826 Answers: 0 Comments: 2

There are two cards; one is yellow on both sides and the other one is yellow in one side and red on the other. The cards have the same probability ((1/2)) of being chosen, and one is chosen and placed on the table. If the upper side of the card on the table is yellow, then the probability that the under side is also yellow is.

$There are two cards; one is yellow on$ $both sides and the other one is yellow$ $in one side and red on the other . The$ $cards have the same probability (\frac{1}{2})$ $of being chosen, and one is chosen and$ $placed on the table . If the upper side$ $of the card on the table is yellow,$ $then the probability that the under$ $side is also yellow is .$

Question Number 111734 Answers: 1 Comments: 0

A chord which is a perpendicular bisector of radius of length 18cm in a circle, has length.

$A chord which is a perpendicular$ $bisector of radius of length 18 cm in a$ $circle, has length .$

Question Number 111732 Answers: 1 Comments: 0

A blind man is to place 5 letters into 5 pigeon holes, how many ways can 4 of the letters be wrongly placed? (note that only one letter must be in a pigeon hole)

$A blind man is to place 5 letters into 5$ $pigeon holes, how many ways can 4 of$ $the letters be wrongly placed ?$ $(note that only one letter must be in a$ $pigeon hole)$

Question Number 111730 Answers: 0 Comments: 9

How many triples of positive integers (x,y,z) satisfy 79x+80y+81z =2016

$How many triples of positive integers$ $(x, y, z) satisfy$ $79 x + 80 y + 81 z = 2016$

Question Number 112813 Answers: 0 Comments: 2

A binary operation has the property a∗(b∗c) = (a∗b)•c and that a∗a=1 for all non−zero real numbers a,b and c. (′•′ here represent multiplication). The solution of the equation 2016∗(6∗x)=100 can be written as (p/q) where p and q are relatively prime positive integers. What is q−p?

$A binary operation has the property$ $a * (b * c) = (a * b) ∙ c and that a * a = 1 for$ $all non - zero real numbers a, b and c .$ $(^{'} ∙^{'} here represent multiplication) .$ $The solution of the equation$ $2016 * (6 * x) = 100 can be written as \frac{p}{q}$ $where p and q are relatively prime$ $positive integers . What is q - p ?$

Question Number 112812 Answers: 0 Comments: 2

There are 2016 straight lines drawn on a board such that (1/2) of the lines are parallel to one another. (3/8) of them meet at a point and each of the remaining ones intersect with all other lines on the board. Determine the total number of intersections possible.

$There are 2016 straight lines drawn on$ $a board such that \frac{1}{2} of the lines are$ $parallel to one another . \frac{3}{8} of them$ $meet at a point and each of the$ $remaining ones intersect with all$ $other lines on the board . Determine$ $the total number of intersections$ $possible .$

Question Number 111725 Answers: 1 Comments: 0

Find the positive integer n such that tan^(−1) ((1/3))+tan^(−1) ((1/4))+tan^(−1) ((1/5))+tan^(−1) ((1/n))=(π/4)

$Find the positive integer n such that$ $\tan^{- 1} (\frac{1}{3}) + \tan^{- 1} (\frac{1}{4}) + \tan^{- 1} (\frac{1}{5}) + \tan^{- 1} (\frac{1}{n}) = \frac{π}{4}$

Question Number 111724 Answers: 0 Comments: 6

How many real numbers x satisfy the equation 3^(2x+2) −3^(x+3) −3^x +3=0 ?

$How many real numbers x satisfy the$ $equation 3^{2 x + 2} - 3^{x + 3} - 3^{x} + 3 = 0 ?$

Question Number 111719 Answers: 2 Comments: 0

....advanced mathematics.... please demonstrate that:: Φ =∫_0 ^( 1) xlog(1−x).log(1+x)= (1/4) − log(2) ... m.n.july 1970 #

$. . . . a d v a n c e d m a t h e m a t i c s . . . .$ $p l e a s e d e m o n s t r a t e t h a t ::$ $Φ = \int_{0}^{1} x l o g (1 - x) . l o g (1 + x) = \frac{1}{4} - l o g (2) . . .$ $You can't use 'macro parameter character #' in math mode$

Question Number 111704 Answers: 1 Comments: 0

Assuming FLT, prove Fermat−Euler theorem: (a,n) =1,n≥2⇒a^(∅(n)) ≡1(mod n)

$Assuming FLT, prove Fermat - Euler$ $theorem : (a, n) = 1, n ⩾ 2 \Rightarrow a^{\emptyset (n)} \equiv 1 (\mod$ $n)$

Question Number 111690 Answers: 1 Comments: 0

Question Number 112534 Answers: 0 Comments: 3

What is the maximum number of points to be distributed within a 3×6 to ensure that there are no two points whose distance apart is less than (√2)?

$What is the maximum number$ $of points to be distributed within$ $a 3 \times 6 to ensure that there are no two$ $points whose distance apart is less$ $than \sqrt{2} ?$

Question Number 111721 Answers: 1 Comments: 0

If b>1,x>0 and (2x)^(log_b 2) −(3x)^(log_b 3) =0, then x is

$If b > 1, x > 0 and {(2 x)}^{\log_{b} 2} - {(3 x)}^{\log_{b} 3} = 0,$ $then x is$

Question Number 111671 Answers: 0 Comments: 0

Question Number 111668 Answers: 0 Comments: 6

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