Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 229

the sum of the series

For x>1 determine the sum of the series

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: the sum of the series

Since it started at x^1, x^6 would not make sense.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

tony123

Member

Registered: 2007-08-03

Posts: 229

Re: the sum of the series

1,2,4,8,16 yes

1,2,4,6 how olivia

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: the sum of the series

If x = 1, the series is

If x ≠ 1, the nth term in the summation is

So the series is

The sum of the first two terms is

Sum of first three terms is

Hence the partial sums are of the form

which → 1 as n → ∞.

By the way, tony123, why do you post all these diabolical problems of yours in the “Help Me!” section? They should be in “Puzzles and Games”.

Last edited by JaneFairfax (2007-12-03 14:34:56)

tony123

Member

Registered: 2007-08-03

Posts: 229

Re: the sum of the series

JaneFairfax
  wonderful Solution
You are right
Next time I shall problem in “Puzzles and Games”

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: the sum of the series

Exercises would work too.

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Why did the vector cross the road?
It wanted to be normal.