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Permutation and CombinationQuestion and Answers: Page 3 |
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Soit x>1. On de^ finie la suite (p_n ) par p_1 =x et ∀n∈IN^∗ p_(n+1) =2p_n ^2 −1 Montrer que lim_(n→+∞) Π_(k=1) ^n (1+(1/p_k ))=(√((x+1)/(x−1))) |
Prove that ∀n∈IN^∗ Σ_(k=1) ^(2^n −1) (1/(sin^2 (((kπ)/2^(n+1) ))))= ((2^(2n+1) −2)/3) Give in terms of n Σ_(k=1) ^(2^n −1) (1/(sin^4 (((kπ)/2^(n+1) )))) |
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If log_a y = (1/3) and log_8 a = x + 1 then show that y = 2^(x + 1) |
given f(x)=cx(x−20) and A=(2,5) find the nearst point to A on the graph |
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∫_0 ^( (π/2)) (((sin((x/2^n )))/(sinx))) dx , n ∈ N |
let S={a,b,c,d,e,f} if we take any subset S (same subset is allowed), it also can be S, which will form S if we join them, order of operation does not matter ({a,b,c,d},{d,e,f}) is the same as ({d,e,f},{a,b,c,d}) how many ways can we choose? |
how is solution lim_(x→sinπ ) ((sin(π/2))/(sinx))=? |
f : [1, 3] →R , f(x) = (1/x) A(1, 1) B(1, (1/3)) B′(b, (1/b)) , b ≥ 1 Find i. equation of line AB′ ii. equation of tangent T ′ to C_f at point with x = ((1 + b)/2) iii. Study relative positions of L_(AB ′) , T ′ to C_f |
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How many non−similar triangles have integer angles in °? |
you randomly select a 5 digit number. what′s the probability that this number has exactly 3 different digits? |
find the number of 5 digit natural numbers with strictly ascending digits whose sum is 20. example: 12458 is such a number |
Find the number of triangles with integer side lengths and perimeter p. |
Given a set H={1,2,3,...,300. We will a create a subset of H consisting of three elements. If the sum of the three elements is divisible by 3 then the number of subsets that canbe made is x. Find the remainder if x is divided by 100000 |
prove for r, n ∈ N Σ_(k=r) ^n ((k),(r) ) = (((n+1)),((r+1)) ) (Hockey−stick identity) |
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C_4 ^4 +C_4 ^5 +C_4 ^6 +...+C_4 ^(26) =? |
Suppose now that Allie is actually 70 years old, and that her life expectancy (if cured) is 12 years rather than 20 . Which procedure now has the greather expected value ? What if her life expectancy is 8 years? |
If two events A and B are such that P(A^c )=0.3 ; P(B)=0.4 and P(A∩B^c )= 0.5 then P((B/(A∪B^c )))=? (A) 0.20 (B) 0.25 (C) 0.30 (D) 0.35 |
How many words can be formed from different letters of the “Your answer is wrong” with not repeating? So that they shouldn′t start with ′o′ neither ′w′ and shouldn′t end with ′w′, and should be′r′ & ′s′ adjacents. Oya...n, Wen...y, Iog...w , Yourws...e : are invalid Enrsow...g : is valid Q.180162 |