GEM T1 C3S4 - Infinite Geometric Series

Open Ended

Find the sum of the geometric series: 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/32768.

Fill in the Blank

What is a + b + c?

Math Response

A girl puts 1 grain of rice in the first square of an 8 by 8 chess board. In the subsequent square, she puts twice that of the previous square, and she continues until she fills all the squares. How many total grains does she need?

Type answer here

Correct Answer: 2^{64}-1

Deg^°

Rad

Multiple Choice

Which part of the summation notation tells you where to start the sum?

• Initial Index

• Final Index

• Sigma

• Summation Term

Fill in the Blank

Fill in the blank: The formula for the sum of the first n terms of a geometric series is

Multiple Choice

Evaluate.

• 290

• 278

• 250

• 295

Multiple Choice

Evaluate.

• 539

• 364

• 346

• 361

Multiple Choice

Evaluate.

• 20

• 28

• 18

• 21

Multiple Choice

Find the sum for the following series. 

• 1.49
• 3.14
• 1.33
• 1.66

Multiple Choice

What is a convergent series?

• A series whose terms approach zero and whose partial sum tends to a specific number

• A series whose terms increase without bound

• A series whose terms alternate in sign

• A series with only positive terms

Multiple Choice

What is the value of the infinite geometric series 1/2 + 1/4 + 1/8 + 1/16 + ...?

• 1

• 0.5

• 2

• Infinity

Multiple Choice

Determine if the series converges or diverges

• Converges

• Diverges

Multiple Choice

Which of the following is DIVERGENT?

• 2+4+8+16+...

• 25+5+1+0.2+...

• 100+50+25+5+...

• 3(0.25)ⁿ = A_n

Multiple Choice

Does the series converge or diverge?

• Converge

• Diverge

• Cannot be determined

Multiple Choice

What is the sum of the sequence 9 + (–3) + 1 + (–1/3) + 1/9 + (–1/27) + ...?

• 9/2

• 27/4

• 9/4

• 3

Open Ended

Find the sum:

5 – 10/3 + 20/9 – 40/27 + ...

Fill in the Blank

The sum 1/2^3 + 1/2^6 + 1/2^9 + ... is ______.

/

Multiple Choice

Find the sum of the infinite geometric series, if it exists. $$\sum_{n=1}^{\infty}8\left(\frac{1}{5}\right)^{n-1}$$  

• 8

• 8/5

• 10

• Does not exist

Open Ended

After learning about summation notation and geometric infinite series, do you have any questions or topics you would like to explore further?

Open Ended

What is one key concept you learned today about summation notation or geometric infinite series, and how might it be useful in real-life situations?