K CK-1) In(k-1) k-3

Q: Serial numbers for a product are to be made using 2 letters followed by 4 digits. The letters are to…

A: We have 5 letters and 10 digits .  We have to choose 2 letters and 4 digits with no repeat.

Q: 's Little Theorm and The Pollard Factorization Metod how could I solve Quetion 4 in Section 6.1

A: Introduction: The product of consecutive integers beginning with that natural number and ending with…

Q: 18) 5-D*n 5n+2 (-1)".n

A: Given∑n=1∞(-1)n.n(5n+2)Now we apply the series divergence testaccording to series divergence testif…

Q: 2-201 0 1 1 1 103 A = 0 1 -1 3 0 1 1 1 1 1 1 Which is the element A3,2?

A: To find the element A3,2  of the given matrix A.

Q: 9. Prove the formula n(n+1) >i =1+2+...+n= 2 i=1

A:

Q: Ix-51>7* O x>7, x 12, x 12 No Solotion

A: We have to solve the inequality

Q: 2 4 8 n2 + 2n 1 (i) 1 3 (ii) (iii) ) - 9 27 1+ 2n2 ' n=0 2nn n=1

A: Both series we can evaluate using geometric series method.

Q: 2. Let, a, = 3, a2 = 4 and for n2 3, a, = 2an-1+ an-2+ 5, express an in terms of n. 3. Let, a, = 3,…

A:

Q: 3 21. (k +1) k=1

A: The given expression is, ∑k=13(k2+1) To find the sum of the expression from k=1 to k=3 substitute…

Q: k+4 n(3n +7) k(k +1)(k + 2) 2(n+1)(n+2) k=1

A: Given ∑k=1nk+4k(k+1)(k+2) To show  ∑k=1nk+4k(k+1)(k+2)=n(3n+7)2(n+1)(n+2)

Q: (-1)*(k – k4/3 ether k=1

A:

Q: (-1)" /n + I is n + 2 n=1

A:

Q: Serial numbers for a product are to be made using 2 letters followed by 2 digits. The letters are to…

A: The serial numbers for a product are to be made using 2 letters followed by 2 digits. The first 6…

Q: 4 22 -62 +ズ+3 3 lim 十ズ +3 ス→1

A:

Q: 49. E (k + 2) 50. E(2k + 1) 52. E (k + 1)2 53. У k=0 3* 51. k= k=1 k=1 k=1 k n-1 n-1 55. E k=0 3*+1…

A: (49) Consider the given expression as ∑k=1nk+2

Q: 3- 2 GL 1- 7654 321 42345 67 -1- -3 723

A:

Q: k It is known that ( + (₁ ²₁₂) + (k) = (²+¹) (k + 1). Prove that r - 2 (k) + ( k + ¹ ) + ( k + ²) +…

A: We will use given formula and value of nr . nr=n!r!×n-r!

Q: 44-16=n-21 What does n stand for?

A: If, a = x - b. Then, x= a + b.

Q: How many terms will be in the expansion of (x – 8y)*" ? There will be 10 – 1 = 9 terms in the…

A:

Q: Serial numbers for a product are to be made using 3 letters followed by 4 digits. The letters are to…

A: Given that the first 3 position of the serial number are 3 letters and then it is followed by 4…

Q: (3/5 +1/5)x(2/4-1/4)=N

A: We want to find the value of N

Q: Induction. 1.3 + 6+9+...+3n= 3n(n+ 1) , for n 1.

A:

Q: 1 4. Σ k-0 (k + 1)(k + 3)'

A:

Q: C=k-2 express ((c^2)-(k^2))-2 in terms of k

A: C=k-2 express ((c^2)-(k^2))-2 in terms of k

Q: k ak ak a-1,a +1 (-1)* 1/½(-1)*+1 kak 4), a +1 a- (ak + b)(n) (ak+b)(n+1) a(n+1)

A: ∆ak= ak+1-ak      = ak(a-1) therefore anti difference of ak=ak/(a-1)

Q: 201-25-(1-82 60 86)(So) | (o-Sh)는 (0-5h4

A: Do square both the side. Now solve 5 powered equation.

Q: third by a fourth power. 8. (Brahmagupta, 7th century A.D.) When eggs in a basket are removed 2, 3,…

A: We use basic module formula here According to the question and then take lcm of all the possible…

Q: '글 +2+글 +5 The sum +8+ +11 written in sigma notation is equal to 8 3k-2 A k=1 2 8 3k - 1 B k=1 8 3k…

A: The sum 1/2 +2+7/2 +5+13/2 +8+19/2 +11.

Q: 3.630 AN(x) 1000- 900- 800- 700- 효 600- 500- arine manufacturer will sell N(x) power boats after…

A:

Q: 1 Σ 4 K(k + 2) k=1 eTextbook and Media

A:

Q: k(z - a)*-1 +0((k +1)(z - a)*) (2 - a)k + O((z - a)k+1)

A: =z-akkz-a-1+Ok+1z-ak1+Oz-a

Q: Determine which property of determinants the equation illustrates.

A:

Q: 1-3 s B/ Determine s2 + 8s + 21

A:

Q: (1+i)²n n! n=0 evaluate

A: The function ex has the expansion ex=∑n=0∞xnn!. The complex number eix=cos x+i sin x.  This is…

Q: gcd(n+1, n) =

A: To Find gcd(n+1,n)=?

Q: 2 n n Σ (2n – 1 п — 1, =n k k=1

A: we have to prove that                                                we know that…

Q: П n -k 1+ i=1

A: Solution is attached below

Q: 1 {a,}={ 4. Let | 2n² Let ɛ =.001. Find a natural number N such that |a, - L<ɛ when n 2 N.

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Q: 0 2५+ 3५-2५-० 24 +4== 364-3647134-

A:

Q: 1 + 5 + 9 +...+ (4n-3) = (2n+1)(n-1) for n ≥ 2 Use proof by Mathematical Induction.

A:

Q: 8. Ση-0 ne-1 4n 9. En=0 (n+2)3 n=0 (n+2)³ 3. 10. Σ0 n-3n+2 %30 n2-3n+2

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Q: where n is a natural number. i(1+1) n+1

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Q: ) Σ 2(-1)"+1 , n In r

A:

Q: 5 Σ (3n + 2)(2n – 1) n = 3

A:

Q: series: n(2n + 5) 8" (n + 1) In(2n + 3)

A:

Q: x-2 If x-N(2,4), then 2 x²(1) O 3 I الخيار 3

A: Given that,  X~N(2, 4)  We have to find the distribution of  x-2/2~..........

Q: η Σ (1) 5 k=1 k odd = 6" - (-4)" 2

A: Here we prove that ∑k=1k oddnnk5k=6n--4n2

Q: Proof 7.4: * Prove k i=0

A:

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.