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Lesson Example Discussion Quiz: Class Homework

Step-1

Title: Infinite sequence and series

Grade: 10-a Lesson: S2-L7

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Find the sum of the infinite geometric series \$S = 4 + 2 + 1 + 1/2 + 1/4 + ...\$ .
2	Formula:	The given series	\$S = 4 + 2 + 1 + 1/2 + 1/4 + ...\$
3	Formula:	The formula for the sum of an infinite geometric series is:	\$ S = a / (1 - r) \$
4	Step	The given series is an infinite geometric series with the first term	a = 4
5	Step	r is the common ratio between successive terms (obtained by dividing any term by the previous term) (2 divided by 4)	In this case, \$r = 1/2 \$
6	Hint	Substituting a = 4 and \$r = 1/2\$, we get:	\$ S = 4 / (1 - 1/2) \$
7	Step	After simplification	\$ S = 4 / ((2 - 1)/2) = 4 / (1/2) = 8 \$
8	Step	Therefore, the sum of the given series is 8.
9	Choice.A	This option implies that the sum of the infinite geometric series is 4. However, our calculation showed that the sum is actually 8, not 4. So, option A is incorrect	4
10	Choice.B	This is not the correct sum of the infinite geometric series with the given terms and common ratio	10
11	Choice.C	This option matches our calculated sum of the infinite geometric series, which is indeed 8. Hence, option C is correct	8
12	Choice.D	This option states that the sum of the series is 12. However, our calculation showed that the sum is 8, not 12. Therefore, Choice D is incorrect	12
13	Answer	Option	C
14	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Find the sum of the infinite geometric series \$S = 4 + 2 + 1 + 1/2 + 1/4 + ...\$ .

Formula:

The given series

\$S = 4 + 2 + 1 + 1/2 + 1/4 + ...\$

Formula:

The formula for the sum of an infinite geometric series is:

\$ S = a / (1 - r) \$

Step

The given series is an infinite geometric series with the first term

a = 4

Step

r is the common ratio between successive terms (obtained by dividing any term by the previous term)
(2 divided by 4)

In this case, \$r = 1/2 \$

Hint

Substituting a = 4 and \$r = 1/2\$, we get:

\$ S = 4 / (1 - 1/2) \$

Step

After simplification

\$ S = 4 / ((2 - 1)/2) = 4 / (1/2) = 8 \$

Step

Therefore, the sum of the given series is 8.

Choice.A

This option implies that the sum of the infinite geometric series is 4. However, our calculation showed that the sum is actually 8, not 4. So, option A is incorrect

Choice.B

This is not the correct sum of the infinite geometric series with the given terms and common ratio

Choice.C

This option matches our calculated sum of the infinite geometric series, which is indeed 8. Hence, option C is correct

Choice.D

This option states that the sum of the series is 12. However, our calculation showed that the sum is 8, not 12. Therefore, Choice D is incorrect

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?