Evaluate the following sum 20 +30).

Q: Expand and evaluate the sum 4 Σ3k +1 k-1

A: Observe that the given expression is the sum of all the terms (3k + 1) where k takes the values from…

Q: Evaluate the sums (i? + 3)

A:

Q: Evaluate the following sums.

A: In this question, we have to expand the double and single summation.

Q: Evaluate the sum. 34 4j2 3 j = 2 196280/9

A: Given that: ∑j=2346j+4j23

Q: Compute the following sum and show your work. 1 2 + -1 3 1 2 -1 2 -1 Can you compute the following…

A: A set of numbers or functions arranged in the form of a rectangular array bounded by the square…

Q: Evaluate the following geometric sum +++ + . . . t 31248 192 12,288

A: Please see the full blown out series on the white board. Let's call the value of the sum of each of…

Q: The fifth term in the sum 10 Σε k 3 k=3 is 83 53 63 73

A:

Q: Compute the following sum: 4· 3i = 4. 32 + 4.33 + ..+ 4·3" %3D i%3D2

A: We need to evaluate the series ∑i=2n4.3i=4.32+4.33+....+4.3n Now, we can take the summation from i=2…

Q: Calculate the following sums: 5 3k а- k=1

A: Use the summation formula:

Q: Evaluate the following sum. 10 10 + 3 10+ + ... 9.

A: First-term = a1 =10  Common ratio = r = second term / first term = (10/3)/10= 1/3

Q: Find of the following the Sum scrics. 2. 1- In(10)+ 2! る!

A: The given series is, y=1-ln10+ln1022!-ln1033!

Q: -3 2( n=4 4.

A: Given ∑4∞2-34n= 2∑4∞-34nhere,∑4∞-34 is an infinite geometric seriesand its first term (a) =-344 =…

Q: Expand and evaluate the given sum:

A: To evaluate ∑i=153

Q: Evaluate the following sums. 8 300 240 (a) 2 (b) Σε Σ 10 8. k=1 k=1 k 3

A: Given : a ∑k=182b ∑k=13008c ∑k=324010

Q: Evaluate the following geometric sum. 1 1 1 1 + ... + 1 + 2 8 32 128 8192 1 1 1 1 + ... + 1 + + 2 8…

A: Given 12+18+132+1128+…+18792

Q: Verify that the geometric sum formula gives the correct result for the sums 1 + (1)/(2) and (1)/(2)+…

A: Formula for the sum of a geometric  series:Sn=a11-rn1-r    r≠1a1=the first termn=number of…

Q: Σ -2-Зп n=5

A: This is an example of infinite Series. We use Divergence Test to show the convergence or divergence…

Q: Express the following sum in closed form. k 4 +3- k=1 Hint: Start by multiplying out ( 4 + 3 . Note:…

A: This sum can be written in the form of an integral sum.Assume that,

Q: k-1,2k k+1

A:

Q: 4. Apply the Sum Formula 1, 2 and 3 to find the sum for n = 13, 15 and 18.

A: The sum formula for n natural number is n(n+1)/2.

Q: Evaluate the following geometric sum. 1 1 1 1 + ... + 1 3 12 48 192 12,288 1 1 1 1 1 + 12,288…

A:

Q: Evaluate the sums. п а. 4 k=1 7 -2k k=1 b.

A:

Q: Write the sum in expanded form. 5 k=2

A: The series is a geometric progression so we have to find out the common ratio, number of terms and…

Q: Determine the sum in (국)". 2n=4

A:

Q: Express the following sum in closed form. 6 +4. n k=1 k Hint: Start by multiplying out 6+4. n Note:…

A:

Q: Express the following sum in closed form. Σ 2 k > (4 +3 in k=1 -(+-2 ). k Hint: Start by multiplying…

A:

Q: Find the following sum:

A: we have to find the sum of the given series. ∑i=130(6i-11)

Q: Evaluate the following sum. -4+5+14+23+32+ .. +176

A:

Q: List the first five terms of the sequence. a1 = 4, an+1 = 5an – 1 a1 = a2 аз az = a4 a5 =

A: Fist five teems of the sequence

Q: Compute the following sums. b. 2+4+8+ 16 + + 1024

A:

Q: List the first five terms of the sequence. а1 3 6, ап+1 %3D 5а, — 2 a1 = a2 %3D az = a4 as = II

A:

Q: Evaluate the following sum. 3+8+13+18+23+ +98

A:

Q: Evaluate the sums

A: Given that: ∑k=15k3225+∑k=15k3…

Q: For Exercise, find the sum. 141 Σ4-4) k= 1

A: We expand the sum

Q: How many 7-letter sequences can be made using the letters in the word U R U G U A Y exactly once…

A: We have to find number of permutations possible.

Q: A. What is the sum of the following: 1.

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

Q: Evaluate the following sum. 5 +7+9+ ... + 27

A: Proceed as shown below

Q: 2) Find the infinite sum if it exists

A:

Q: Rewrite the following as a single sum: 12 12 E (3k – 9) + 3D (ho – 3) + 8 k=2 k=8 k=2 i=1

A: First, we try to write it as one sum.…

Q: Find the sum of the first 12 terms of the arith metic seauence 20,18,110,..

A:

Q: Compute for the sum. Answer directly. Lore ΣΣ (-)) i=1j=1

A:

Q: List the first five terms of the sequence. aj = 5, an+1 5а, - 6 5an %3D aj = a2 = %3D a3 = a4 as |3|

A:

Q: Use the approach on Gauss's problem to find the following sums of arithmetic sequences…

A:

Q: Calculate the values of the following serics. 4+ 2" a ) Σ b) (-2)" 3n en n=0 n=1 Hint: write it as a…

A: Given: a)∑n=0∞4+2n3nb)∑n=1∞(-2)nen

Q: 12(5" (8") n=1

A:

Q: Evaluate the following sum. 5 +7+9+... + 27

A: We know the formula to find the sum of first n terms of an Arithmetic Progression is S = n/2[2a + (n…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.