Expand the following sums and simplify 1. E-2 (i3-2i) Solution: Vi D. Li=0 -4 Solution: E2 (12-i)(3i) Solution:

Q: Find a formula for n in terms of m where: n is a length in feet and m is the length in inches.Note…

A: We have to find a formula for n in terms of m where n is a length in feet and m is the length in…

Q: Find the indicated sum. 6 j= 1 Σ- j= 1

A: We want to find the indicated sum.

Q: (b) Find the sum of each of the following series. 00 (i) > nx", , |x| < 1 n = 1 (ii) Σ 3n 8.

A: i).  To determine the sum of infinite series given by; ∑n=1∞nxn,|x|&lt;1 Consider the series…

Q: How many terms are needed to estimate 10+(-1)".n 5n (- to n=0 within 0.1? Justify your answer!

A:

Q: Find the infinite sum (if it exists): (-) 6 . 7 i=0 If the sum does not exists, type DNE in the…

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Q: Evaluate the following geometric sum. 3)k Σ k=0 ..... 3 Σ %3D k=0 (Do not round until the final…

A:

Q: Express the function below in series form. 1 1+ 8x2 a. Σ n=1 Ob. n=0 00 (8x n=0 Od. >(-8x?)" n=0

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 6. (5ai² – 7bi+ 3c) :2 i=4

A: We have to find the sum for the given series.

Q: Solve for ar, given the geometric series 20 1

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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: Find the indicated sum.

A: Given:             ∑k-3k=14k+2 First term: k =1           a1=1-31+2    =-2.3    =-6 Second term: k =…

Q: Find the indicated sum.

A: Consider the provided series, ∑i=1∞-25i-1 Find the indicated sum. The provided series is geometric…

Q: Find the sum of the series 12+17+22+..+777

A: We have to find the sum of the series 12+17+22+....+777. First term=a=12 In the arithmetic…

Q: Compute each sum below. If applicable, write your answer as a fraction. 4 + 4 +... + 4 %3D %3D j = 1…

A: Given that: 4+4-12+4-122+...+4-125∑j=19(4)j

Q: B. Solve for the indicated term of each expansion. 3. The term involving x* of (+52

A:

Q: Find the sum. 38 > (2n + 1) n=1 1482

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Q: Find the indicated sum. 6 Σ E 9k k= 1

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Q: Find the sum using formulas: 371 Σ

A: Given that: ∑k=8837112

Q: Evaluate the series 8 2 (3n – 4) n=1 O Campfire Mocha -1 76 20

A: In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol…

Q: Use the fact that Σ nxn-1 to find the sum of each series. (1 - x)2 in (a) n = 1 ΗΣ E(9)'-C (b)

A:

Q: Evaluate the following sum. E(-1+2i)² i=1

A: Given: ∑i=1n(-1+2i)2

Q: Find the indicated (shown) sum:

A: Given: ∑i=14-12i

Q: Find the exact sum of the series…

A:

Q: Find the value of the following series 1 a. Ση=3η2_2n

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

Q: 3. For what value of r does the series 1+r+r² + r³ + • = 10 ?

A:

Q: Find the indicated sum.

A: Given that ∑ i=14 -12i. Compute the sum as follows.

Q: > (4i? – 7i) =3

A: Given:

Q: Find an expression for the following sum in terms of r and n: n Ei.(-r)i-1 i=1

A: First calculate ∑i=1nxi using GP sum:  ∑i=1nxi=xxn-1x-1

Q: 2. Find the sum V2+ V99+V100

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Q: Write the terms of the following sums. 1j+2

A: See below.

Q: How many terms are required to ensure that the sum is accurate to within 0.0002? e-n n=1

A: We have to find the number of terms required for the sum to be accurate within 0.0002 .

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: Determine how many terms of (-1)*+lgk must be summed to be sure that the remainder term k! k=1 is…

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Q: Find the following sums without using a calculator. Apply the procedure used by Gauss.      1 + 2 +…

A: Find the sum    1+2+3.+4+.......+397+398+399+400 by applying the procedure used by Gauss.

Q: Find the sum S given by S=1² +2²x+3x²+4² x³ +0 for x < 1

A: A good problem. We shall look at the famous geometric series \sum x^n and obtain S by repeated…

Q: For each of the following repeating decimals, determine the fraction in lowest terms represented by…

A: For each of the given repeating decimals we have to determine the fraction in lowest terms…

Q: Use the figure below and the triangle sum theorem to find the value of x. 2x +11 55°

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Q: For Exercise, evaluate the sum if possible. (2i-1

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Q: 5 E (i- 4) i = 1 in

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Q: There is a simple formula for the sum of the first n cubes. n' (n + 1)2 n i=1 Using this formula,…

A: Sum of cubes

Q: Use a sum or difference formula to find the exact value of the following

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Q: Solve for the sum for the following:  ∞ Σ      [(-1^n)*π^(2n+1)]/[(4^(2n+1))*(2n+1)] n=0

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Q: Evaluate the following geometric sum. 1 1 1 1 10 20 40 + ** + 320 1. 1 1 1 10 20 40 320 (Simplify…

A: The sum of a geometric sequence is given by the formula, sn=a1-rn1-r where a is the first term of…

Q: Find the units digit for the sum 1325 + 481 + 5411.   Note: Solve the problem following Polya’s…

A: Polya’s Four Step Method.  Understand the problem. Devise a plan. Carry out the plan. look back…

Q: Write each summation as a series. (3i-2-1) i=2

A:

Q: Evaluate the sum algebraically: E 2i* – 11i 064

A:

Q: How many positive or equal equatror n mx=lm elements does the nez:1m

A: We have to find the number of elements in the set  m∈ℤ:1≤m∈6750,mx≡1mod 750

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.