12 + 22,., +n? =n(n+ 1)(2n + 1), Vn eN

Q: Q1-let A = 6a B - ; ) [2 3 & B = Verify that (AB)" = B" A"

A: Explanation of the solution is given below....

Q: 7 Evaluate using Convolution theorem: L-¹{²(²+4)} 2

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

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

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Q: 4|\B Prove that (V3+ i)6 = -64

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Q: Q.2. Proof that V= u8--

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Q: A submarine attempts to sink an aircraft carrier. It will be successful only y two or more torpedoes…

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

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Q: P is of degree 2; P(0)=4; zeros -1, 4?

A: Write the standard form of polynomial with the help of zeros.

Q: Proved Ax (BNC) = (AX B)n (AXC) %3D

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Q: Find z-transfrm for (n-1) X(n) u(n-1) x (n) 5nucn) - 2 n (o.3) uci) 2)

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Q: 3. Let, a, = 3, a2 = 4 and for n2 3, a, = 2an-1+ an-2 + nº+ 1, express a, in terms of n.

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Q: Let n € Z. Prove that if 2 | (n² – 5), then 4 | (n² – 5). Solution:

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

A: The nth term of A.P is given by an=a+n-1d we have,  a=3,d=4-3=1an=3+n-11=2+n we get,…

Q: b) Prove that 20 15 k Σ 3.2-Σ 96.2 %D i=5 k=0

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Q: 1- Suppose A=

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Q: 1S prove that (a + b) = a² + b².

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Q: 6. Show that Vz eC i) z-7 is a real number. ii) (z-2) is a real number.

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

A: we have the nth term of A.P is given by  an=a+n-1d here,  a=3, d=4-3=1an=3+n-11=2+n we get,…

Q: * :The nth term formula for { 1,0,1,0,... } is 1-(-1)" 2. an = A₂ = An خيار 2 1 + (−1)" 2.

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

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: 2. What is the quotient of and?

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Q: show that V2+V5 is irrational num ber

A: Solve the following

Q: EIf a,,a,,a,.--,a, be an A P of non - zero terms, prove that ------ 1 1 +. 1 n-1 %3D a,a, a,a, a,a,

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Q: Va +3b + Va – 3b If x=- Va+36 – Va– 3b prove that 3bx² – 2ax +3b = 0 | - -

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Q: How to proof: R2=(Cov(X,Y)/SxSy)2

A: R2 is defined as the co-efficient of determination, which determines whether the fit of our…

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

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

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Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1 +an-2 +n², express an in terms of n. %3D

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Q: If x1=3, ,x2=3, xn=−6xn−1−5xn−2, ∀n≥3x1=3, ,x2=3, xn=−6xn−1−5xn−2, ∀n≥3. Find the general tem xn

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Q: -2/2] 2 3) If A= and B 2 2v21. Show that A and B commutative.

A: The two matrices A and B are said to be commutative if AB=BA. The given matrices are…

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

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Q: Solve for n if nEN: (4+8+12+ ... +4(n-1)) + (2+4.5+7+. .. 4+5n -%3D126.5 2

A: Sum of n natural numbers is n(n+1)/2.

Q: Q2/ prove [A] [A] = [I] if [2 4 -5 [A]= 2 7 1 3 4

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Q: Prove that r(1/4) r(3/4) = /27. %3D

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Q: 51 3 -[---] -4 2 -2 Let u= (a) 5u-2v, 3 V= 5 W= -1 Find:

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Q: 5. For non-negative integer n and r, where 1<rsn, show that (n-r+1)"C,1=n(""C,). r-1

A: Given n and r non negative integers with  1≤ r≤ n. We need to prove (n-r+1)nCr-1=n(n-1Cr-1)

Q: Let X=(1,0, – 1,- /2)'. Then, ||X||, = Select one: а. -V3 O . 2+V2 C. -V2

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Q: Given: 5(2x – 8) = 30; Prove: x = 7 -

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

A: We will find out the required expression in the term of n.

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

A: An arithmetic progression is a sequence of numbers such that the difference d between each…

Q: 8. Prove 3n e R|n? – n < 0

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

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Q: Q4: 1- Prove that (1– i)? + (1+ i)² = 0 . %3D 2- Put in the form a + ib ((1+ i)²)² - ((1- i)²)².

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

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Q: 3) Calculate: AВ-ВА , АС-СА , ВС-СВ Where 1 1 0 1 A 1 1 B -1 1 0 0 V2 Vzi 1 0. 0 -1 0. -1

A: I have found each product term one by one

Q: 0. Prove that (i) |4' ||, =||4||,, and (ii) ||4' A|| -||4|-

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Q: 27 1 2-r2 4. Evaluate: r dz dr de Jo

A: Solution

Q: (b) Show that V n 20 > (2i +3)3' = (n+ 1)3"+1. i=0

A: To Show- Show that ∀ n ≥ 0 ∑i=0n2i + 33i = n + 13n+1.

Q: (16) Show that AB=BA for 1 5 0 0 A = 0 3 0 0 0 and B = 3 1 2

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