Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**3rdMath****Member**- Registered: 2013-01-29
- Posts: 1

Given the series 1/2 + 1/(2^4)+1/(2^7)+1/(2^10)

(i) show that this is geometric sequence..........can some1 help with this please

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,951

Hi;

That is a geometric series because each term has a common ratio which is

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **Thinking is cheating.**

**Online**

**n872yt3r****Member**- Registered: 2013-01-21
- Posts: 392

(2^4=16) (2^7=49) (2^10=100) 1/16+1/49=0.0829081632653061224489795183673...+1/100=0.09290816326530612244897959183673...+1/2=0.59290816326530612244897959183673...

- n872yt3r

Math Is Fun Rocks!

By the power of the exponent, I square and cube you!

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 15,954

n872yt3r wrote:

(2^4=16) (2^7=49) (2^10=100) 1/16+1/49=0.0829081632653061224489795183673...+1/100=0.09290816326530612244897959183673...+1/2=0.59290816326530612244897959183673...

That is not correct. 2^7 is not 49 and 2^10 is not 100...

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,951

Hi n872yt3r;

7^2 = 49 and 10^2 = 100

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **Thinking is cheating.**

**Online**

**mttal24****Member**- Registered: 2012-05-01
- Posts: 23

Well, to identify and prove a geometric progression the following can be used:

If

t2/t1=t3/t2=t4/t3=.....=tn/t(n-1)=r (and 'r' also represents common ratio)

then the sequence is a GP.

Here,

1/2^4 divided by1/2 is equal to 1/2^7 divided by 1/2^4.

Thus, you can show that it is a gp

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,378

hi 3rdMath

Welcome to the forum.

If you had an algebraic form for the general term, then you could do the job in one go with

As you have just 4 terms and no general term you will have to show that

The value for this constant has already been given in earlier posts.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

Pages: **1**