Consider the sum: 3 E(-1)*(k +2)² – 1). k=0 (A) Which of the following expresses the sum without sigma notation: (1) 22 – (1 + 2)² + (2 + 2)² – (3 + 2)² – 3 * -1 (2) 22 – 1– (1+ 2)² + 1 + (2 + 2)² –- 1 – (3 + 2)² + 1 (3) 22 – 1 – (1+ 2)² – 1 + (2 + 2)2 – 1 – (3 + 2)? – 1 Enter the number 1,2, or 3: (B) Evaluate the sum:

Q: Find r(t) and v(t) if a(t) = tk, v(0) = 15i, r(0) = 14j.

A:

Q: -1)*+1 Ln=1 ¯n•I0* O error| < 2 × 10 -6 O error| < 2.5 × 10-6 O error| < 2.5 × 10–5 O error| < 10-5

A: Given: ∑n=1∞-1n+1n.10n. All the options have 6th term expanded. Therefore, we will check for , n=6.…

Q: B. Write the following as summations: 1. a₁ + a₂ + a3 + a4 +a5 2. v6+v7 + V8 + V9 + V10 3. 4m3 + 4m4…

A: Sigma : the symbol of summation

Q: se the summation notation to rewrite the following expression (13 − 9) − (23 − 9) + (33 − 9) − (43…

A:

Q: Expand and simplify. (8h +3) (7h² – 4h+1) - O 56h3 – 32h² + 8h + 3 - O 56h3 – 11h? 4h + 3 O 56h3 +…

A:

Q: Express the following sum in closed form. 5n(n+1) 2 n Σ (5k – 3) k=1 = Note: Your answer should be…

A:

Q: Rewrite 1/2(x-5) +1/4(x-5)2 +1/6(x-5)3  +1/8(x-5)4 using summation notation.

A:

Q: (- 1)"x" Σ 6" (n² + 9) n=1 8.

A: Given

Q: 00 (2n +1)" n2n n=1

A:

Q: Find n(A)   A= {1/2, -1/2, 1/3,- 1/3,......1/10, -1/10}

A: Compute n(A) as follows.Assume a set B with 20 elements.B = {1,−1, 2, −2, 3, −3,......10, −10}.

Q: h(n) = 4n – 1 g (n) = n² - n Find (h o g) (4n)

A: Consider the functions  h(n)=4n-1g(n)=n2-n

Q: Q1. find the sum by adding each term together. (3i + 2) i=1 1 k2 + 1 k=0

A: ∑i=163i+2 ∑k=041k2+1 ∑ck=07

Q: Use the summation notation to rewrite the following expression (13 − 9) − (23 − 9) + (33 − 9) − (43…

A:

Q: Find the sum of 1/7 + 3/7 + 32/7 + 32 /7 + ⋅⋅⋅ + (3)n-1 / 7

A:

Q: Which of the following is a false statement? In the expansion of (a +b) the coefficient of a b° is…

A: We have to choose the false statement.

Q: 5. Which of the following is (a) n! n=1 80 (b) n=1 (c) E T=D1 (d) -1)" (2n)! T1

A: We have to find out the power series

Q: και Σ(+1-143) (b) Evaluate the sum i=1

A:

Q: Find the sum 1 9k2 + 12k – 5 k=1 Express your answer as a rational expression in terms of n.

A:

Q: Write using summation notation:(>) 6 4 5 + + 3! 4! 5! 13 -+.. (12)! 3.

A: Given that, The series in term of summation notation is denoted by, Where an is the nth terms of…