Find and evaluate the sum. Σ-1)*1 4k k=2 Σ-1)14k= k=2 (Type an integer or a simplified fraction.) Find and evaluate the sum. Σ-1) j= 4 Σ-1 -| j= 4

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: Example 8: 50 Find the sum (3i + 4)

A: We have given a sequence  ∑i=150( 3i+4) Put i = 1  So first term,a=3+4 = 7 Put i = 2  So second term…

Q: 7 Evaluate the sum i(3i + 2) i=1

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Q: 43 Compute for the sum. Answer directly. 2 3 ΣΣ11;3 i=0j=0

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Q: Can i get help step by step with this problem?

A: The given sum is,

Q: 1 Calculate the sum + 5 - j=-1

A: See the attachment.

Q: 1. Find a formula for the sum: 2+ 6+ 10 ... + 2(2n - 1)

A: The given sequence is 2+6+10+... +2(2n–1).

Q: 1-) Qu+2-3Qu+1+2Qu=5     Q0=1 Q1=1 find the rule of series

A: The given equation is,Qu+2-3Qu+1+2Qu=5---(1) with Q0=1 and Q1=1Substituting u=u-2 in (1) we…

Q: The ration of the sums of m and m terms of an AP is m2:n2 .show that the ratio of mth and nth  is…

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Q: 4) Evaluate the sum. Et=2(3k – 21)

A: Given K=2,3,4

Q: Evaluate the sums

A: Given:

Q: 4-)Qu+2=2(Qu+1-Qu)  Q0=1 Q1=2 find the rule of series

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Q: In each case, find the first 5 terms of the sum and compute S, 3. The sum 1S 2 The first 5 terms are…

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Q: 1 The sequence an %3D 2n +3 (a)decresing (b) in

A: See the details solution in below

Q: Use sigma notation to write the sum. 5 8 8 [(;)³ - ;];) + . ² ] ( ² ) + n Σ i = 1 Additional…

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Q: Find the sum of 73 ㅈ5 11.3 3.5 ㅗ ㅈ - + ㅈㄱ 15.7 + n-1_2n+1 ㅈ (1)h 12n-1 (2n+1)

A: We can solve as follows

Q: Can i get help step by step?

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Q: How would you represent the sum 3+7+11+15+ 19 with the sigma notation?. (4k – 1) k-0 (k + 4) k-3…

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Q: 3. Determine the sum 3. 42n+1 (a) 33n n=1 4.5n-1 ( b) Σ 32n+3 n=1

A: to find: Sum of the given series

Q: Find the sum, if it exists. 11 k Σ 13 k = 1 2/3

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Q: Induction. 1.3 + 6+9+...+3n= 3n(n+ 1) , for n 1.

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Q: 4. Let n >1 be an integer. Consider the following expression 3 (3* – 212 + 2) – 2 (3* – 3k2 + 2) k=1…

A: Let's find.

Q: Use sigma notation to write the sum. 3 3 + 3n 3n + n Σ i = 1

A: Use the summation notation to write the given series.

Q: .3.4 .45 Find the sum. - 1- 13- 169- 2197 - ...- (13)" Sn = (Simplify your answer.) %D

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Q: 5. Given >U, = 3n(n +1) calculate the sum r=1 of ten terms starting from the eighth term.

A: Solution: Given that

Q: 30 (a) Find the sum of 2k+1. k=2 (b) Show that if Re z < 0, then Je| <1 and find the sum of ) ek*.…

A: i have given the formulas that i have used in the step where i have used them

Q: Write out the sum. n-1 1 Σ gk +1 k=0 Find the first, second, third and last terms of the sum. n-1 Σ…

A: The given sequence start from n =0 so to find nTh term we have to put k = n-1. For example for first…

Q: 2. Find the sum. 1 4 3 4 3 Oundefined 1

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Q: 08. The sequence { GT) }n-1 3n+2 37+1

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Q: Choose all those that represent the sum 5+7+9+11+13+...+101. 101 Σκ k = 5 50 E (2K+ 1) j = 2 50 Σ…

A: We have to find the correct representation of the sum 5+7+9+11+13+⋯+101

Q: Determine the sum in (국)". 2n=4

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Q: Write out the sum. n- 1 1 Σ 3k+1 k= 0 Find the first, second, third and last terms of the sum. n- 1…

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Q: Use the rules for sums of powers of integers to compute the sum. 24 4.² k=8

A: Recall: sum of squares of n integer                    ∑i=1ni2=n(n+1)(2n+1)6

Q: 8. Which containment is true, if any (A denotes the symmetric sum.) (An B)AC C or 2 (AAC) N (BAC).

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Q: Use sigma notation to write the sum. [금)-(금)·. ()-끝() 9 (4) 3 3 3n 3n 3 + n Σ i = 1

A: Look at the question there is a variable multiplied with 3 inside the square bracket which is…

Q: Use Gauss' trick to determine the sum 1+3 + 5 +... + (2n – 3) + (2n – 1) + (2n + 1

A: Gauss's trick is very significant in determining the sum of a series. This method includes the…

Q: what is the summation where k = 1 of e^-2k

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Q: #2. Find the sum of the 8 n=1 1 (3n+ 1)(3n+4)

A: In given series we break the nth term of series as addition of nth term of two different series…

Q: 12. Find the sum. Σ2-15k) k=4

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Q: Find the indicated sum. (-1)k*1 Σ (k+1)! k =0 (-1)k*1 (k+1)! -0.63 (Type an integer or a simplified…

A: we have to find

Q: (a) Evaluate the respective sum and product. 4 2" (i) E en É 2n+2 (i) П n=0 п n=1

A: Solution: (i) ∑n=042n2n+2

Q: 10. Use the formula (3k-1)(k-4) = n-5n²-2n, V ne Z* to calculate k-1 20 the sum (-6)+ (-10) + (-8) +…

A: given (-6)+(-10)+(-8)+0+⋯+840+944=∑k=120(3k-1)(k-4)we have given the formula…

Q: 5.) Find the sum. 73 > (8n + 1) j=4

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Q: Write out the sum. 2 (k+6) k= 1 Find the first, second, and last terms of the su in I (k + 6) =D•+O…

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Q: Mrs. Hill asked her students to express the sum 1+ 3+ 5+ 7+9+...+ 39 using sigma notation. Four…

A: Since , the given sum is 1+3+5+7...+39 So its a alternate odd numbers sequence with end number is…

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

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Q: Use the approach in Gauss's Problem to find the following sums of arithmetic sequences.  A.…

A: Consider the series 1+2+3+4+…+1001. For the series 1+2+3+4+…+1001, it is clear that there are 1001…

Q: A sequence is said to be an increasing sequence if .... Vn 21 .a O n+1" n S =SbO n+1 n+128.cO 2n.dO…

A: sequence (an) is: strictly increasing if, for all n, an &lt; an+1; increasing if, for all n, an ≤…

Q: Consider the sequence 1 4 4' 5' 6' 7 1 2 1 2n-2 1 0, ... a2n-1 a2n 3 2n-1' 2n Which of the following…

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Q: 2. Use the Geometric Sum Formula to do the following. (a) Evaluate 1 +3+3² +3³ + · ·.+310. (b) (Part…

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