Math Is Fun Forum

shivusuja

Member

Registered: 2006-09-14

Posts: 56

sequences and series

please help me out  with this two problems.

If  G.P consists of an even number of terms. I the sum of all terms is 5 times the sum of terms occupied by odd places, then find its common ratio.

If let S be the sum , P the product  and  R the sum of reciprocals of n terms in a G.P . Prove that  P^2R^n=S^n

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: sequences and series

If the GP has first term a (which presumably is ≠ 0) and common ratio r, the odd terms in the progression form another GP, with first term a and common ratio r[sup]2[/sup]. So you want to find r such that

Since r ≠ ±1 (why?) both a and n should drop out of the equation on simplification and you should be able to find r.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: sequences and series

For the second part, the reciprocals of the GP is a GP with first term 1⁄a and common ratio 1⁄r; hence

which simplifies to

So

Also we have

Now put ’em all together.

Last edited by JaneFairfax (2007-10-19 10:03:06)

Avon

Member

Registered: 2007-06-28

Posts: 80

Re: sequences and series

Surely we should have:

Don't you just love it when two mistakes cancel each other out.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: sequences and series

shivu said:"If  G.P consists of an even number of terms. I the sum of all terms is 5 times the sum of terms occupied by odd places, then find its common ratio."
Answer is 4.
(4 + 1)/1 = 5.

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