Use Leibniz's method to find the sum of the series 2² +9² +16² +23² + ... +72² Suggestion: This is the series (2+0(7))²+(2+1(7))² + (2+2(7))²+...+(2+ (x − 1)(7))² You must show your work for credit.

Q: For the sequence an = n +1' its first term is its second term is its third term is its fourth term…

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Q: Find the sum of the series: 1 + 4 + 7 + 10 + ...+ 43

A: Sum of n natural number is n(n+1)/2

Q: Determine the sum of the series n² +2n n=1 Write your answer as a numerical value in decimal form.

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Q: ind b3 for the sequence generated by the sequence br+1 = 3b,, bo = 2. A) 27 В) 54 C) 6 D) 162 For…

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Q: Find the generating function for the sequence 1,−2,4,−8,16,….

A: The general expansion of the binomial (1-x)-1 will be, (1-x)-1=1+x+x2+x3+….

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: What is the sum of the geometric series:  4 + 4 x 3 + 4 x 33 + 4 x 33 + ... + 4 x 314?

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Q: Consider the sum (3)2 + (8)² + (13)2 + +(15n-2)2: ... (a) Write the sum in sigma notation.

A: Consider the sum  (3)2+82+132+.....................+(15n-2)2

Q: nd the following sum: 2 + 4 + 6 + 8 + ... + 88 using Gauss' method. Show all ste

A: To find the below sum using the Gauss' method. 2+4+6+8+...+88

Q: Find the sum of 1 + 3 + 9 + 27 + … to 12 terms.

A: =1+3+9+27+...+n.  in this a1=1,a2=3            r=a2/a1=3/1=3            s=(a(rn -1))/(r-1)…

Q: Consider the sequence 2, 7, 12, 17, 22, 27, ..., 5n - 3. How many terms are there in the sequence?

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

Q: What role do partial sums play in defining the sum of an infinite series?

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Q: Write the series using summation notation. -3 + 4 - 5+6-7 Σ i i=1

A: Given series is Let the nth term of the series is  then, In general, for n=1,2,3,4,5, we have

Q: Find the sum of1/1 · 3 +1/3 · 5 +1/5 · 7 +··· .

A: The given series is, 11.3+13.5+15.7+..... Consider the first term, 11.3=12×1-12×1+1 Consider the…

Q: How is the series 5 + 8 + 11 + ... +77 represented in summation notation? 25 ΟΣ(3q + 5) q=0 17 ΟΣ(4q…

A: Given Series is  5+8+11+........+77

Q: Find S9 for the series 7 + (-21) + 63 + (-189) + ...

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Q: sum

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Q: .  Identify the series and determine the sum of (3x+2y)+(5x+2y)+(7x+2y)+...+a10 2. In the geometric…

A: This is a AP and GP problem

Q: Find the sum of each finite series. (2n-1) 22. (3n+2) 23. -2

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Q: Use the approach in Gauss problem to find the sum of 8+17+26+35+...+890

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