PLEASE HELP ME!

1. What is the sum of the series?

∑i=153i

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2. What is the sum of the series?

∑k=14(2k)2

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3. What is the sum of the series?

∑k=36(2k−10)

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4. Which answer represents the series in sigma notation?

1+14+116+164+1256+11024+14096

∑j=174j−1

∑j=1714j+1

∑j=17(14)j−1

∑j=1714(j+1)

5. Which answer represents the series in sigma notation?

−5+(−1)+3+7+11

∑j=155j−1

∑j=15−5⋅(15)j−1

∑j=15(4j−9)

∑j=15(−6j+1)

The sigma notation allows writing an expression in a compact form using the upper and lower boundaries of the variable, then the actual expression. The solutions to the problems are as follows.

1.)

; values of i ranges from 1 - 5 ;

2.)

; values of k ranges from 1 - 5 ;

= (2×1)² + (2×2)² + (2×3)² + (2×4)²

= 4 + 16 + 36 + 64

= 120

3.)

; values of k ranges from 3 - 6;

= (2(3) - 10) + (2(4) - 10) + (2(5) - 10) + (2(6) - 10)

= - 4 - 2 + 0 + 2

= - 4

4.)

The common ratio, r = r2 ÷ r1 = r3 ÷ r2 = r4 ÷ r3 =...

r = 1/4 ÷ 1/1 = 1/4

The nth term of a geometric sequence :

Hence, the series in sigma notation can be expressed thus :

5.)

This is an arithmetic series :

d = -1 - (-5) = -1 + 5 = 4

nth term = a + (n-1)d ; n = number of terms ; a = first term

General expression :

-5 + (n - 1)4

-5 + 4n - 4

4n - 9

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Step-by-step explanation:

The simplest method is "brute force".  Calculate each term and add them up.

∑ = 3(1) + 3(2) + 3(3) + 3(4) + 3(5)

∑ = 3 + 6 + 9 + 12 + 15

∑ = 45

∑ = (2×1)² + (2×2)² + (2×3)² + (2×4)²

∑ = 4 + 16 + 36 + 64

∑ = 120

∑ = (2×3−10) + (2×4−10) + (2×5−10) + (2×6−10)

∑ = -4 + -2 + 0 + 2

∑ = -4

4. 1 + 1/4 + 1/16 + 1/64 + 1/256

This is a geometric sequence where the first term is 1 and the common ratio is 1/4.  The nth term is:

a = 1 (1/4)ⁿ⁻¹

So the series is:

5. -5 + -1 + 3 + 7 + 11

This is an arithmetic sequence where the first term is -5 and the common difference is 4.  The nth term is:

a = -5 + 4(n−1)

a = -5 + 4n − 4

a = 4n − 9

So the series is:

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.