1. Using induction, prove that 2 (^(^^!) ) ² २ 2 3=1 J 3

Q: B Gven AB II DE Prove AABC^ADEC A

A:

Q: Find L[et tsin(2t) - e-2t+3 +e-2t cos 3t]

A: BY USING THE LAPLACE TRANSFORMATION RULES  WE GET OPTION (D) IS CORRECT OPTION.

Q: n be a positive natural nun (an)" is equivalent to: 4n Let a) n²n (n²-4n) b) n(n²^_^) d) na^ (^^-2^)…

A: Given, n4n-(2n)2n

Q: Prove by induction E 3₁ = (3^+¹ -1) 2 i=o

A:

Q: (Proof by cases: (p₁ V P2 V (Pn →q)) Prove or disprove. V Pn) → q = (P₁ → q)^(p2 →q)^^...^ "The 4th…

A: Let x be any integer.  We need to prov        x4 does not leave remainder 2 when divided by 3.…

Q: What is the exponent on the x variable of the 3st/nd/rd/th term in the expansion of 17 (x2 +3y)" ?…

A: using formula:-

Q: Click and drag expressions to show that Ln= fn−1+fn+1 for n=2,3,..., where fn is the nth Fibonacci…

A:

Q: If g(t) = £? (e-35-*), a farmula for L (e* g14) is? -8t +8 a) ede+25 b) e 3e+17

A: Given g(t)=ℒ-1e-3s-7

Q: Prove-that '(2) r' (₂+1) ¹ (2+ |) T(₂) nd thus derive Legendre's duplication formular 2' (2) T(2:)…

A:

Q: 3. From Fermat's theorem deduce that, for any integer n 20, 13| 1112+6 + 1.

A:

Q: If C₁ * x² = c(1) ²¹ + a₂ (1) ²³ t² is the complementary solution of the nonhomogeneous system 3…

A: If the nonhomogeneous system is x'=3-22-2x+-2tt4-1 If the complimentary solution is…

Q: prove the following identities k(nk) = (n-1k-1) (n0)+(n1)+(n2)+ .... ..... +(n n-1) + (nn) = 2^n…

A:

Q: a/2 2. Evaluate f[(e)i-2sin(t) j+3cos(1)k]dt

A:

Q: Show that /(-1)-7(1) but there is Let f(x) 1 Show that /(-1) (1) but there is no number e in (-1, 1)…

A:

Q: Va 占>0 !! に

A:

Q: Show thet the Se nng + ベ+」 (+リ(2ペ+)+ ()) (ox) ナ (A+)(2p+1) (P+1) (28+1)(38+) (uhse a>0, B70) (uhse…

A: A series is said  to converge  if  the sequence of partial sums  converge. There are various tests…

Q: Find the coefficient of a' in the expansion of: (a) (1 – x)-4x (c) x²(1+ x²)*(1– x)-3 (b) (1 – x)-2x…

A:

Q: How did they go from 30(2^k-1) to 15(2^k)? Please explain

A:

Q: Let k be the order of "a" in n mode, then prove that, o(ah) = k (h, k) = 1

A:

Q: Prove that 3! 2(n+3) = = n r=0 (-1) 1 n "Cr r+3 Cr

A:

Q: For n is greater than or equal to  1, use mathematical induction to establish each of the following…

A:

Q: Prove that there exists an n ∈ N such that 7 | (3^n − 1).

A:

Q: How many ways are there to distribute r+s identical balls among five different children such that…

A:

Q: If a and b are integers with gcd(a, b) = d Then gcd (-- d.

A: Given a statement

Q: [ *(1 + 2') dt = 1 + 2°) dt 14 + C In(7) In(14) 14t+1 In(14) 7t+1 + C In(7) 7t In(7) 9t + C In(9) +…

A: Given:       ∫ 7t(1+2t)dt

Q: Find [7]^-1 in Z55 under multiplication.

A:

Q: What is the Coefficient o x' y b. 24 in (3x +y)? Plow monomials appear in +he meny expansion of (3x+…

A:

Q: n —(2) - (-) (1)¹(1)(). (n-1)

A:

Q: (2) Give a proof by contradiction of theorem “If n^2+1is odd, then n is even”

A: The given problem is to prove by using the contradiction of Theorem of the given statement. Given…

Q: 2 + х2 — 1 х — 1 х+1 5х 1

A:

Q: Use the Binomial Theorem to expand the expression (3x + 2y). Show your work.

A:

Q: For what value of k is x+1 a factor of x^4+2x^3-3x^2+kx+1 in ℤ_5[x]?   1 2 3 4 None of the above

A:

Q: (п-1)! d) DE (x"-1nx)

A:

Q: (b) Express x +1 4 as a single fraction in its simplest form. x- 2 3.

A:

Q: expand about z=1 (z+1)(z-2)*

A:

Q: EC»(a-p)- = Ip + (1- p)" = 1" = 1.

A: