The sum of n,2n,3n terms of an AP are S1,S2,S3 respectively.Prove that S3=3(S2-S1)

Q: Q5: prove 1) e2-j3n-e² = 2) |e²| = ex

A:

Q: Find all integer solutions 2² – 2y? = 22 satisfying (x, y, z) = 1.

A:

Q: Determine the particular solution1 1. (2-r) dr=rsin 0 de; when 0 0 and r 1

A: The given differential equation is 2-r2dr=r2sinθdθ. Rewrite the above differential equation as…

Q: Oa, 1+ 16a, 2+ 225n for n> 2 with initial conditions ag = -23, a1 -19.

A: Given recurrance relation is  an=16an-2+225n     , n≥2 and initial conditions are a0=-23, a1=-19

Q: Q1(i) Prove that 1 1 1 + 2n²+1 V2n2+2 V2n2+n]

A: To prove: lim 12n2+1+12n2+2+.........+12n2+n=12

Q: (b) Define fo = 0, f₁ = 1 and fn = fn-1 + fn-2 for n ≥2. Show that 3 fak for all k ≥ 0.

A: As per the guidelines we shall solve one question only as you have asked more than one different…

Q: Σ n=1 5n Vn3 +1

A:

Q: Find a formula for sn, n > 1, if s, is given by 2 3 4 6 - - - 3' 5'7' 9 ' 11

A: We have to find Sn

Q: Prove that Ek=0 C) 7n-k . 2k = 32n %3D

A:

Q: Q D 2. Identify the missing information necessary to prove that TV 1 SU S O <SVT ZUVT O ST SV ST UT…

A: Given:     Triangle Figures is given

Q: Use the substitution method to show that the solution of T(n) = 2T(n/3) + n2is O(n2)

A: Given that T(n)=2Tn3+n2 To show that it is O(n2).

Q: 41. If yo Yı • Y2 , Y6 are the consecutive terms of a seies, ..., then prove that Yz = 0- 05 (yo+…

A:

Q: 5. Find the sum of the first 10 terms of An, where 1, and a2 an 2aп-1 + an-2, а1 %3D %3D = 1.

A:

Q: Prove that E, k2* = (n – 1)2"+1 +2 for all n > 1. =D1

A:

Q: f in a AP the sum of m tern=ms is equal to n and the sum of n terms is equal to n then prove that…

A:

Q: 2. Prove that, for all k E N, 2 can be written as the sum of two squares.

A:

Q: Ex : Express the Sum o+ 2 +4+6+8 in Sigma nata tion. K = -2 %3D -2

A: First we find nth term of AP then replace k by k+3

Q: Now we assume that P(r) is true, that is, r can be written as a sum of 3s and 5s, for any cases,…

A: We are given a statement and its proof. We need to answer two questions about the proof. More…

Q: Show that MP-1 (n) + (m+1) Pm+1 (n). - (2m +1) " Pm (n] =>

A: The objective is prove that mpm-1x + m+1pm+1x - 2m+1 x pmx = 0. To show the given result we will use…

Q: Prove m3 – n° = (m – n) (m² + ²). - N m - n (m – n)(m² + mn + n° Enter your next step here %3D 2.

A:

Q: Find x for which det(A)=0 7-x -2 A = 1- x 0. 5- x The sum of the answers is....

A: See the detailed solution below.

Q: If m*n Denofes -3伝 + Find the 2mn?

A: Given that m*n=2m-n2 therefore -3*5=2-3-52

Q: Suppose that q # 1 is a constant. Calculate the sum n Sn =E kg* = q+ 2q² + 3q³ + • ..+ ng" k=1

A:

Q: Hew.2 Exfress the Summ ef the Vecturs AB and if ACl,-1)_, B (2,022C(-l,3) and D(-2,2).

A:

Q: n! Verify that Ex1+…+xr=n,xi20 r^n for any r, n>1 x1!x2!...xr!

A: Consider the given information. Let n is greater than equal to 1 arbitrary. Use the mathematical…

Q: Find the least value of “n" so that , k=n 1 199 Sn 2k-1 k=1 200

A: Given:          Sn=∑k=1n12k−1&gt;199200

Q: Find A and B if -1 L-1 5 s + 1 s² – s –12 `12 إجابتك

A:

Q: [Hint: For m > 2, ( 2 7. For n > 1, verify that + 1 1² + 3² + 5² + ... + (2n – 1)° = ( 2"" ) - 8.…

A: Let's say we need to prove a formula or a statement P(n). To prove this, we need to prove that The…

Q: The sum of n,2n,3n terms of an AP are S1,S2,S3 respectively ,Prove that S3=3(S2-S1)

A:

Q: Prove using INDIRECT PROOF: 1) P → Q 2) R → S 3) ﬢQ ۷ ﬢS ﬢP ۷ ﬢR

A: The statements given are as follows: P→QR→S~Q∨~S For the first statement, we will apply the…

Q: Q(x) = √3/2+² Ser fet de Prove that & QQ (-∞ ) = 1

A: Here we can use Gamma function formula Γn = ∫0∞ xn-1 e-x dx to evaluate the given improper integral.…

Q: John give 2/3 of his pencils, P, to Roy and then gives 1/4 of the pencils t he has left to Maria. In…

A:

Q: If z, = 5ej®1 , z, 3e182 , determine all solutions of 01 and 02 so that z, + z2 = 4.

A: Consider the provided question,

Q: (b) Verify that 17(s +1) (s² – 2s – 3)(s2+2s +2) s+5 (s – 3) (s2 +2s +2)

A:

Q: (x – 2)² – In x = 0, [1,2]

A: Follow the python script.

Q: Find a formula for Sn, n > 1, if sn is given by 6 7 3' 5' 7' 9' 11 4 8 - Sn =

A:

Q: & B= Q1-Let A = 2 4 Verify that (AB)" = B" A"

A: As per our guideline we are supposed to do 1 question at a time. Please post other questions next…

Q: she has gotenng.uf of $2.60. 13lina is Saved. She hos a' C AlL of her Change dime S, or quaters, She…

A: Elina is gathering up change that she has saved and these are total $2.60. All of her change is in…

Q: Find integers s and t so that s· 201 + t · 302 = 1 . S %3D

A:

Q: Q1) Compute the products using the definition as a linear combination. 8 3 -4 1 2 1 5 1

A: As per the definition of linear combination abcdef.x1x2x3=x1.ad+x2.be+x3.cf

Q: 3 and for n > 2, an = 2an-1+5, express an in terms of n. 1. Let, a1

A: The solution is given as

Q: 4 and for n > 3, an 2an-1 + an-2 + 5n, express an in terms of n %3D 2. Let, a1 = 3, a2

A:

Q: If m*n denotes Im-n2 find the value of j. 3* (2*1)

A:

Q: Solve the recursion by substitution for  T(n)=2T(n/4)+n2 where T(1) =1

A: To solve by putting T(1)=1

Q: A culture containing 16 bacteria doubles every day. Which of the following formulas represents the…

A: topic - exponential function

Q: The sum of Hthe first S=3n²+4a fFinal+he li mit an is nlmits ofar plogression an arthmctic

A: