(-7)(-7 – 1)(-7 – 2)(–7 – 3) (7) | | (a) 4 4! 210 7/2 (b) (7/2)(7/2 – 1)(7/2 – 2) 3 3! ||

Q: PROVE: Z3 = 26 k 2 4 3 a 5 8 7 b LO

A: Given:

Q: Using appropriate methods to show that 1. 5x2 +3x-2 dr r(x+ 2)2 In a + 6 In |r + 2| + +C. (r+2)

A:

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: Question- The expression (x^2-5x-2)-(-6x^2-7x-3) is equivalent to Can you pleaseee do this fastt and…

A: Two second digree polynomial is given as a subtraction. We have to perform the operation by opening…

Q: the statement below true or false for n=1? ©George Mason University 2+ 4 + 6+ ... + 2n = n² + n + 1

A:

Q: -2{-12/-3+2[2²-12-√100]-(3²)}

A: We want to solve the given basic mathematical operation problem.

Q: (п - 2)аn+1(2х — 3)п+1 + > ап-1 (2х — 3)"-1 n=0 n=2

A:

Q: inconclusive. n² +1 2n +1

A:

Q: how that the given statement is true. (1) - („")-- (?) - rst we can show that n! (1) - 1([ ow we can…

A: Our objective is to prove the given statement.

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

A: To find if ∑k=3∞kk-12lnk-1 is convergent or divergent: ∑k=3∞kk-12lnk-1 is convergent. To show this…

Q: (2n- 2. Give a combinatorial argument to show that k- ways the number of ways to select a committee…

A:

Q: Suppose ne N. Then the following equation is true: () - ) -)-) - + (-1 = 0. + 3 How can this…

A: Let's find.

Q: Fibonacci number is true or false. 3Fn > Fn+3 for n = 3

A: Solution :-

Q: 1 0 0 0 0 1 2 -6 2 -8 10 1 0 1 0 3 -2 -5 -16 |

A: We have to multiply: 1000012-60010003-22-8-5-16

Q: Subtracting (10u³ – 3u² + 4u +9) from (5u² – 7u + 12) the result is O -10u³ + 8u² – 1lu + 3 O 10u³ +…

A: Do the algebraically substraction. Substract the numerical terms of each variables of similar terms…

Q: 2) S(n)-10-2 at n 5

A: Given ,  f(n) = 10 (2)n     ......... (1) We have to find the value at n = 5 Put ,  n = 5 in…

Q: Using a combinatorial argument (proof), demonstrate that: {.";} - () - «()(;) n – 2 +.5 n

A:

Q: JESTIC True or False: For all n EZ, n +5n +2 is even. True False

A:

Q: 1-3-5...(2n–1) n=1 3"n!(2n+1)

A: As it can be seen that only the first one is incorrect. So, we will be solving it. Here,         .

Q: In z - 3[4ln (z - 6) - In (z + 6)] z(z + 6)4 In g(9 - z) z(z- 6)3 In (z + 6)4 z(z + 6)4 In (z - 6)4…

A:

Q: Ž (1 – p)?k=1 = -P- Ž (1 – p)²k 2k-1 Ë (1 – p) | 1- P k=1 k=1

A: Considering the LHS looping the values from 1 to 4 ∑k=1∞(1-p)2k-1 = 11-p∑k=1∞(1-p)2k LHS…

Q: "Statistically Z-Test can be used if the sample is large ( n > 30 ) even population SD is not…

A: Z test:  Z test is a test statistics where the sample mean is standardized assuming the null…

Q: An investigator was interested in the most effective way to teach college algebra. He assigned his…

A: Here the two groups are Independent, one is younger students and other is older students

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

A: We want to find the value of N

Q: . 2+ 4 +6+8+ 10 + ·… + 2n = n+ n² . 1+8+ 27 + .. + n³ = n² (n + 1)2 2+5+8+ ... + (3n – 1) = ;n(3n +…

A: Here is the solution of the given problem. Mathematical Induction Method:

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

A:

Q: 4  Prove: ¬A -> (B -> ¬C) ¬D -> (¬C -> A) D ∨ ¬A ¬D -------------------- ¬B

A:

Q: Give a combinatorial proof (an algebraic proof will not be accepted ()()-(")- (;) 2n n 2 . -2. 3 3

A:

Q: 2. What Is the sum of 3z+7 + ? -16 8x2-22x-18 (2+4)(2+5)(z-4) » #-4, z-5, T#4 822-22z+18…

A:

Q: 1.); 'n+1 2.1)n+1 (-1)n+1 n! (2х)^-1 3.) '(2n-1)5 4.)1)"-1 n+1

A: a) 1/2,1/3,1/4 b)2/3,3/5,4/5 c)1,2,3 d)6/9,7/11,9/12

Q: 2.4.6 . ·(2n) Σ n x". 1.3.5..... (2n – 1) n=1

A:

Q: > (atan (2n – 1) – atan (2n +3)) n=0

A:

Q: 2n+2 – 3" Σ - 2. Determine 6n+1 n=0

A: To find: ∑n=0∞2n+2-3n6n+1

Q: n²-7n +3 | + 10n-4n2 n2 4 + n3 In (n+2) in(1+4n)

A:

Q: 1 1 + 3*5 1 1 n ... 1*3 5*7 (2n-1)*(2n+1) 2n+1

A:

Q: 2x1 — Зх1 — 5х2 — 7хз + 3x4 3D 11 4x1 + 3x2 — 4xз — 5х, 3D 3 5x1 + 4x2 + 6х3 — 2х4 3D 45 2х2 + 3x3 +…

A: We have: 2x1-2x2+3x3+4x4=333x1-5x2-7x3+3x4=114x1+3x2-4x3-5x4=35x1+4x2+6x3-2x4=45 This can be written…

Q: 3 5 3 (A) 2 · 8 7 1 5 %3D 8 4 1 1

A:

Q: (– 1)n+1x2n+2 n=1 3n+1(2n+ 1)! (– 1)"-1x²n-1 Σ n=1 30-1(2n - 2)! Some other answer (– 1)"+1x2n+3 Σ…

A: We have to choose the correct answer from the given option

Q: The simplified value of the expression 2^(2q-1) + 3^(2q-1) when q = K+1 is   1. 8^K + 27^K   2.…

A:

Q: 2(-1)n-1_6" n=1 5n+1

A: To find: ∑n=1∞-1n-16n5n+1

Q: Prove that each of the statements below is false by finding a counterexample. a) For all x and ye R,…

A: a) It is false Answer(a): The given statement is false. (Proved)

Q: true or false: When testing H0: u = – 8 against H1: u > – 8, the power of the test is greater for μ1…

A: GIven, H0: μ = -8 Vs Ha : μ > -8       To Check, the power of the test is greater for μ1 = – 6…

Q: Questionl:- 3 0 -2 -2 Suetch the evaluate egon of mtgradam and

A: ∫03∫-20(x2y-2xy)dydx First integrating with respect to y,  ∫03x2y22-2xy22-20dx…

Q: Using Wilson's Theorm, Fermat's Little Theorm and The Pollard Factorization Metod how could I solve…

A: We have to find the remainder when 7·8·9·15·16·17·23·24·25·43 divided by 11.

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

A:

Q: 8 - 6 ÷ 2 + 3 x 5 7 x 3 - 15 ÷ 5 8 + 2( 1 + 12 + 2)? 3 + (7 - 5)? x 6

A: Solution-

Q: 5 Σ (3n + 2)(2n – 1) n = 3

A:

Q: 4 i. 9-n+24n+1 n2 + 4n + 3 n=1 2n + 1 ii. > n²(n + 1)2 n= 4 iii. と2+3n + 2 n=2 |

A: