Question

PLEASE HELP ME 20 PTS
Consider the series Three-halves + three-fourths + StartFraction 3 Over 8 EndFraction + StartFraction 3 Over 16 EndFraction + ellipsis

What expression defines Sn?

S Subscript n Baseline = 3 (one-half Superscript n)
S Subscript n Baseline = three-halves (one-half Superscript n)
S Subscript n Baseline = 3 (1 minus one-half Superscript n)
S Subscript n Baseline = three-halves (1 minus one-half Superscript n)

Answer 1

Answer:

The answer is C

Sn=3(1-1/2^n)

Step-by-step explanation:

Answer 2

The expression which defines $S_{n}$ is option c which is $S_{n} =3(1-1/2){n}$.

What is geometric progression?

A geometric progression is basically a sequence in which all the terms have a common ratio. It is also known as G.P.

How to find sum of G.P.?

We have been given a sequence as 3/2+3/4+3/8+3/16+.....

If we carefully see the sequence then we will find that this sequence is a Geometric progression because there is a common ratio between all the terms that is 1/2.

Ratio of first and second term=3/4/3/2=1/2

We know that Sum of GP when n<1 is $a(1-r^{n} )/1-r$

we have to just put the value of =3/2 and r=1/2 in the above formula.

$S_{n}$=3/2(1-$1/2^{n}$)/1-1/2

=3/2(1-$1/2^{n}$)/1/2

=3*2/2(1-$1/2^{n}$)

=3(1-$1/2^{n}$)

Hence the expression which denotes $S_{n}$ is 3(1-$1/2^{n}$).

Learn more about geometric progression at https://brainly.com/question/12006112

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