-5, -3, -1, 1, ....; sum of reciprocals is 16/63: find numb.

[lisaz0224]

I know what this problem is asking, but I don't understand how to do it. Can you please tell me how to do it, but not the answer?

A number pattern begins -5, -3, etc. with numbers increasing by 2 each time. The sum of the reciprocals of the terms is 16/63. How many terms are in the pattern?

I know that you can just keep adding and checking, but I don't think that's a very efficient way.

Thanks!!

 

[mmm4444bot]

Arithmetic Sequences and Partial Sums ...

Hi Lisa:

Are you familiar with arithmetic sequences and their partial sums? How about Sigma Notation?

A sequence is a set of numbers written in a specific order (such as -5, -3, -1, 1, 3, 5, ...).

There are methods to write formulas for generating the nth number in a sequence.

There are methods to find the sum of the first n numbers in a sequence.

Sigma Notation is a handy way to abbreviate these sums.

If none of this rings a bell, then try searching on keywords at Google: "arithmetic sequence find partial sum".

If you are familiar with these topics, then please post what you know about starting this exercise, and we can go from there.

Cheers,

~ Mark

 

[Deleted member 4993]

Re: Another Problem...

I know what this problem is asking, but I don't understand how to do it. Can you please tell me how to do it, but not the answer?

A number pattern begins -5, -3, etc. with numbers increasing by 2 each time. The sum of the reciprocals of the terms is 16/63. How many terms are in the pattern?

I know that you can just keep adding and checking, but I don't think that's a very efficient way.

Thanks!!

Hint:

\(\displaystyle \frac{16}{63} \, = \, \frac{1}{7} \, + \, \frac{1}{9} \,\)