Question and Answers Forum

AllQuestion and Answers: Page 67

Question Number 216279 Answers: 1 Comments: 3

Question Number 216274 Answers: 0 Comments: 0

prove that : Σ_(n=1) ^∞ (( cos( n ))/n) ( 1+(1/( (√2))) + (1/( (√3))) + ...+(1/( (√n))) ) is convergent.

$$ \\ $$$$\:\:\:{prove}\:{that}\:: \\ $$$$ \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:{cos}\left(\:{n}\:\right)}{{n}}\:\left(\:\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\:+\:...+\frac{\mathrm{1}}{\:\sqrt{{n}}}\:\right) \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:{is}\:\:\:{convergent}. \\ $$$$ \\ $$

Question Number 216270 Answers: 2 Comments: 0

If (b − c)x + (c − a)y + (a − b)z = 0 then prove that ((b − c)/(y − z)) = ((c − a)/(z − x)) = ((a − b)/(x − y)) .

$$\mathrm{If}\:\left({b}\:−\:{c}\right){x}\:+\:\left({c}\:−\:{a}\right){y}\:+\:\left({a}\:−\:{b}\right){z}\:=\:\mathrm{0}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\frac{{b}\:−\:{c}}{{y}\:−\:{z}}\:=\:\frac{{c}\:−\:{a}}{{z}\:−\:{x}}\:=\:\frac{{a}\:−\:{b}}{{x}\:−\:{y}}\:. \\ $$

Question Number 216266 Answers: 1 Comments: 0

(√2)^((√2)^((√2)^⋰ ) ) =?

$$\sqrt{\mathrm{2}}\:^{\sqrt{\mathrm{2}}\:^{\sqrt{\mathrm{2}}\:^{\iddots} } } =? \\ $$

Question Number 216265 Answers: 0 Comments: 0

Question Number 216263 Answers: 0 Comments: 1

Question Number 216253 Answers: 1 Comments: 1

If x is a positive acute angle and sinx + sin^2 x + sin^3 x = 1 then find minimum value of cot^2 x.

$$\mathrm{If}\:{x}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{acute}\:\mathrm{angle}\:\mathrm{and} \\ $$$$\mathrm{sin}{x}\:+\:\mathrm{sin}^{\mathrm{2}} {x}\:+\:\mathrm{sin}^{\mathrm{3}} {x}\:=\:\mathrm{1}\:\mathrm{then}\:\mathrm{find} \\ $$$$\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cot}^{\mathrm{2}} {x}. \\ $$

Question Number 216251 Answers: 0 Comments: 0

Find the smallest value of the expression ⌊((a+b+c)/d)⌋+⌊((b+c+d)/a)⌋+⌊((c+d+a)/b)⌋+⌊((d+a+b)/c)⌋ (a,b,c,d)∈N

$${Find}\:{the}\:{smallest}\:{value}\:{of}\:{the}\:{expression} \\ $$$$\:\lfloor\frac{{a}+{b}+{c}}{{d}}\rfloor+\lfloor\frac{{b}+{c}+{d}}{{a}}\rfloor+\lfloor\frac{{c}+{d}+{a}}{{b}}\rfloor+\lfloor\frac{{d}+{a}+{b}}{{c}}\rfloor \\ $$$$\:\:\left({a},{b},{c},{d}\right)\in{N} \\ $$

Question Number 216245 Answers: 1 Comments: 7

Question Number 216242 Answers: 0 Comments: 0

(x−a)^2 +(x^2 −a)^2 =a^2 Find x, given a.

$$\left({x}−{a}\right)^{\mathrm{2}} +\left({x}^{\mathrm{2}} −{a}\right)^{\mathrm{2}} ={a}^{\mathrm{2}} \\ $$$${Find}\:{x},\:{given}\:{a}. \\ $$

Question Number 216239 Answers: 4 Comments: 3

Question Number 216367 Answers: 1 Comments: 0

Question Number 216363 Answers: 0 Comments: 2

Question Number 216230 Answers: 1 Comments: 0

Question Number 216226 Answers: 0 Comments: 1

please check the qurstion out guys

$$\mathrm{please}\:\mathrm{check}\:\mathrm{the}\:\mathrm{qurstion}\:\mathrm{out}\:\mathrm{guys} \\ $$

Question Number 216219 Answers: 2 Comments: 1

Question Number 216207 Answers: 0 Comments: 2

Prove that any kind of equation should have atleast one root. (Algebric fundamental theorem)

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{any}\:\mathrm{kind}\:\mathrm{of}\:\mathrm{equation}\:\mathrm{should} \\ $$$$\mathrm{have}\:\mathrm{atleast}\:\mathrm{one}\:\mathrm{root}.\:\left(\mathrm{Algebric}\:\right. \\ $$$$\left.\mathrm{fundamental}\:\mathrm{theorem}\right) \\ $$

Question Number 216202 Answers: 4 Comments: 0

prove : sin(a+b)=sin(a)cos(b)+sin(b)cos(a)

$${prove}\::\: \\ $$$${sin}\left({a}+{b}\right)={sin}\left({a}\right){cos}\left({b}\right)+{sin}\left({b}\right){cos}\left({a}\right) \\ $$

Question Number 216201 Answers: 1 Comments: 0

Question Number 216188 Answers: 3 Comments: 0

Question Number 216178 Answers: 2 Comments: 0

B = ((3^4 + 3^2 + 1)/(3^7 - 3)) + ((4^4 + 4^2 + 1)/(4^7 - 4)) + ... + ((10^4 + 10^2 + 1)/(10^7 - 1)) Find: B + (1/(220)) = ?

$$\mathrm{B}\:=\:\frac{\mathrm{3}^{\mathrm{4}} \:+\:\mathrm{3}^{\mathrm{2}} \:+\:\mathrm{1}}{\mathrm{3}^{\mathrm{7}} \:-\:\mathrm{3}}\:+\:\frac{\mathrm{4}^{\mathrm{4}} \:+\:\mathrm{4}^{\mathrm{2}} \:+\:\mathrm{1}}{\mathrm{4}^{\mathrm{7}} \:-\:\mathrm{4}}\:+\:...\:+\:\frac{\mathrm{10}^{\mathrm{4}} \:+\:\mathrm{10}^{\mathrm{2}} \:+\:\mathrm{1}}{\mathrm{10}^{\mathrm{7}} \:-\:\mathrm{1}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{B}\:+\:\frac{\mathrm{1}}{\mathrm{220}}\:=\:? \\ $$

Question Number 216183 Answers: 1 Comments: 0

Question Number 216180 Answers: 4 Comments: 0

Question Number 216164 Answers: 2 Comments: 0

Question Number 216162 Answers: 1 Comments: 0

Question Number 216161 Answers: 1 Comments: 0

Pg 62 Pg 63 Pg 64 Pg 65 Pg 66 Pg 67 Pg 68 Pg 69 Pg 70 Pg 71

Contact: info@tinkutara.com