Math Is Fun Forum

teo

Member

Registered: 2007-08-04

Posts: 7

sequences and series problem

the first term of a geometric series is 8. the sum of its first ten terms is 1/8 of the sum of the reciprocal of these terms. find the common ratio.

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to take the first step is easy, to climb up the mountain is another matter.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: sequences and series problem

I just guessed and tried it out.
If you want the answer click on button.

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JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: sequences and series problem

Let the common ratio be r.

Then notice that the reciprocals of the first geometric series form another geometric series with first term 1⁄8 and common ratio 1⁄r.

Hence using the formula for sum of terms

Solve this and you should get r = 1⁄2.

I just guessed and tried it out.

Guessing may work sometimes, but it is by no means a method I would give as a foolproof advice to people who need help with their problems. The problem isn’t that tricky anyway – all you need is to know the formula for the (finite) sum of terms of a GP.

Last edited by JaneFairfax (2007-08-05 00:35:47)