Prove that Σ n1+n2+n3=n (₁ ₁) (-1)³₁-² n n1 N2 N3 (-1)^1-n2+3 = 1, where the summation extends over all nonnegative integral solutions of n₁ +n₂+ n3 = n.

Q: 2. Let x1x₂ >. (1+x₁) n . xn> 0 ben real num 1 + x₁ + x1x2 + .. + x1xz

A:

Q: x - x3 + x² – x + 1 is reducible over Q True False

A:

Q: a. Σχy, i=1 b. Σ(x)(y) C. (Σ' (Σ'

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Show that Sn is solvable when n ≤ 4.

A: Given: Sn. We have to show that Sn is solvable when n≤4.

Q: Prove & [a+(i-1)d] =na + dn(n-1) where a and d are fixed real numbers. 2 n Use the properties of…

A: To prove :- ∑i=1na+i-1d=na+dnn-12

Q: If n^2+6n+11 = x^2+y^2 for positive integer n, x and y prove [xy/2] is composite. Note: [t]…

A: Given :              n2+6n+11 = x2+y2              t ≤ t

Q: Show that z / [(z-1)(z-3)] = -3 Σ [(z-1)n / 2n+2] - [1 / (2(z-1))] for 0 < |z - 1| < 2.

A: by using techniques of partial fractions and series expansion of 1/(1-x)

Q: Use a sum formula to find tan() 12

A:

Q: Show that when |z +1| < 1,z² =1+£(n +1)(z+1)" n=1

A:

Q: Show that F0F1 . . . Fn−1 = Fn − 2 for all n ≥ 1, where Fi is the i-th fermat number

A: To Show -

Q: (a) Prove that for n ≥ 2, 3 > 2n + n². (b) For any n ≥ 1, the factorial function, denoted by n!, is…

A:

Q: Prove that product notation d/n = nτ(n)/2.

A:

Q: n² -1) 2n³ + 1

A: ∑n=1∞ -1nn22n3+1 use the alternating series test an=n22n3+1 an is positive and monotone decreasing…

Q: /128 V72 (a) Simplify (b) Simplify 5 V3 1+V3 3+2/3' 1 giving your answer as a fraction with an…

A:

Q: Q.4) Find the value of Sigma (d=sum of student id + 22, and c=12) 4c(d + x)(7c* +2cz +9z*) ((d +x)*…

A: As the student ID is not provided, I assume the sum of the digits are 10 (say). Then d=10+22=32 and…

Q: Σ s2 an convergent or divergent?

A:

Q: Prove that ( n2 + 1) / (n + 1) diverges to +∞

A: Let

Q: In this question, you may have to multiply two formal infinite sums. Given En2o ant" and Enzo bnt"…

A: As per the question we are given a recurrence relation as : F(n) = F(n-1) + (n-1) With initial…

Q: Indicate the least integer n such that f(x) = (3æ³ + 2x²)(5æ5 + 4æ*) € O(x").

A: Finding f(x) explicitly using multiplication of polynomial. The highest power of x or degree of f…

Q: 1 Use convolution theorem to evaluate L-1 (s²+9)²)

A:

Q: - ₂ F₁ (-m. a + m;c; x) = +++(c + m) -r (c) dm [x²+m-¹ (1-x)²-c+m] m

A:

Q: Prove that x" dx „n+1 + C, n + 1 for n + -1.

A:

Q: 1+ 3k 1- 3k] 1 – 3k 1+3k 2 - prove that AK: 2 1 For A : -1 -

A: Given, A=2-1-12   ...i    ....(i)  We need to show that Ak=121+3k1+3k1+3k1+3k    ...ii     Now, A…

Q: {In(8n+1) – In(4n +5)} 20. b. 0 c. In(2) d. In(5) e. Divergent а. 2 с.

A: ln8n+1-ln4n+5 Now, limn→∞ln8n+1-ln4n+5=limn→∞ln8n+14n+5…

Q: Prove that 2n+l > (n + 2) · sin(n) for all positive integers n.

A:

Q: Q3 A) Write the first five terms of the following: - 2. {1- (-1)") (3n+2 B) Determine which of the…

A: "since you have asked multiple question,we will solve first question for you.If you want any…

Q: Let q1, q2, q3, . . . be defined by q1 = 2, qn = 3qn−1 − 1 for n ≥ 2. Show by induction that for all…

A: We are given a sequence of qn and we have to use induction to prove that : qn = 1/2(3n + 1)