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Question Number 60416 Answers: 0 Comments: 0

Sum the series: ^n C_0 ^n C_1 + ^n C_1 ^n C_2 + ^n C_2 ^n C_3 + ... + ^n C_r ^n C_(r + 1)

$$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}:\:\:\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{0}} \overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{1}} \:+\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{1}} \overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{2}} \:+\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{2}} \overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{3}} \:+\:...\:+\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{r}} \overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{r}\:+\:\mathrm{1}} \\ $$

Question Number 60413 Answers: 1 Comments: 4

Question Number 60410 Answers: 0 Comments: 2

lim_(x→0) [(x^2 /(tanxsinx))] [.]=grestest integer function

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{{x}^{\mathrm{2}} }{{tanxsinx}}\right]\:\left[.\right]={grestest}\:{integer}\:{function} \\ $$

Question Number 60406 Answers: 1 Comments: 0

n ∈ Z^+ , Find the coefficient of x^(−1) in the expansion of (1 + x)^n (1 + (1/x))^n

$$\mathrm{n}\:\in\:\mathbb{Z}^{+} ,\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\:\mathrm{x}^{−\mathrm{1}} \:\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\:\:\left(\mathrm{1}\:+\:\mathrm{x}\right)^{\mathrm{n}} \left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{n}} \\ $$

Question Number 60398 Answers: 0 Comments: 3

I am very sorry mr W sir for taking your valuable time thank you very much i got my mistake. I will work on my basics thank you and I am very sorry.

$${I}\:{am}\:{very}\:{sorry}\:{mr}\:{W}\:{sir}\:{for}\:{taking}\:{your}\: \\ $$$${valuable}\:{time} \\ $$$${thank}\:{you}\:{very}\:{much}\:{i}\:{got}\:{my}\:{mistake}. \\ $$$${I}\:{will}\:{work}\:{on}\:{my}\:{basics}\:{thank}\:{you} \\ $$$${and}\:{I}\:{am}\:{very}\:{sorry}. \\ $$

Question Number 60386 Answers: 1 Comments: 4

lim_(x→0) ((sin(πcos^2 x))/x^2 ) why it can not be solved this way lim_(x→0) ((sin(πcos^2 x))/x^2 ) =lim_(x→0) ((sin(πcos^2 x))/(πcos^2 x))×lim_(x→0) ((πcos^2 x)/x^2 ) =π × lim_(x→0) ((cos^2 x)/x^2 ) but it is not equal to π

$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{sin}\left(\pi{cos}^{\mathrm{2}} {x}\right)}{{x}^{\mathrm{2}} } \\ $$$${why}\:{it}\:{can}\:{not}\:{be}\:{solved}\:{this}\:{way} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{{sin}\left(\pi{cos}^{\mathrm{2}} {x}\right)}{{x}^{\mathrm{2}} } \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{{sin}\left(\pi{cos}^{\mathrm{2}} {x}\right)}{\pi{cos}^{\mathrm{2}} {x}}×\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{\pi{cos}^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} } \\ $$$$=\pi\:×\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{cos}^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} } \\ $$$${but}\:{it}\:{is}\:{not}\:{equal}\:{to}\:\pi \\ $$

Question Number 60384 Answers: 0 Comments: 0

∫e^(coth^(−1) (x)) dx

$$\int{e}^{{coth}^{−\mathrm{1}} \left({x}\right)} \:{dx}\: \\ $$

Question Number 60376 Answers: 1 Comments: 2

Question Number 60370 Answers: 2 Comments: 0

Question Number 60367 Answers: 0 Comments: 6

Question Number 60362 Answers: 0 Comments: 1

Question Number 60340 Answers: 0 Comments: 0

Question Number 60337 Answers: 0 Comments: 2

15,25,42,...?

$$\mathrm{15},\mathrm{25},\mathrm{42},...? \\ $$

Question Number 60335 Answers: 0 Comments: 0

find I_n = ∫ x^n arctan(x)dx with n integr natural.

$${find}\:{I}_{{n}} =\:\int\:\:{x}^{{n}} \:{arctan}\left({x}\right){dx}\:\:{with}\:{n}\:{integr}\:{natural}. \\ $$

Question Number 60330 Answers: 0 Comments: 1

Question Number 60354 Answers: 0 Comments: 0

Question Number 60351 Answers: 0 Comments: 2

Question Number 60357 Answers: 0 Comments: 1

Question Number 60347 Answers: 1 Comments: 1

Question Number 60346 Answers: 0 Comments: 1

∫xsec^3 xdx please help

$$\int{x}\mathrm{sec}\:^{\mathrm{3}} {xdx} \\ $$$${please}\:{help} \\ $$

Question Number 60322 Answers: 1 Comments: 2

Question Number 60321 Answers: 0 Comments: 2

Question Number 60320 Answers: 0 Comments: 1

Question Number 60319 Answers: 0 Comments: 0

Question Number 60318 Answers: 0 Comments: 2

Question Number 60439 Answers: 2 Comments: 1

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