Pre-calc help

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steph7

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Find in terms of a & pi, the sum of the first 50 terms of the series: a+pi, a^2+2pi, a^3+3pi...where a is a fixed real number.
 
What have you tried? Remember, we're here to help you, not to replace you.

I'd split it into two sums: (a + pi) + (a^2 + 2pi) + (a^3 + 3pi) + ... + last term = (a + a^2 + a^3 + ... + last term) + (pi + 2pi + 3pi + ... + last term).

Each part should be a familiar type. Can you find the two sums?
 
Hint: Arrange the terms in the series into a geometric and arithmetic series:

[MATH]S_n=\sum_{k=1}^{n}(a^k)+\pi\sum_{k=1}^{n}(k)[/MATH]
Can you proceed?
 
I already split it apart, I understand how to do the arithmetic part the pi, 2pi and so on. But is the sum for the geometric part the a, a^2... just a? I’m using the formula.
 
steph7 said:
I already split it apart, I understand how to do the arithmetic part the pi, 2pi and so on. But is the sum for the geometric part the a, a^2... just a? I’m using the formula.
Click to expand...
That "using the formula" business always worries me. There is no substitute for know where it came from and what it actually does.

[math]a + a^2 + a^3 + a^4 + … + a^n = [/math] What? How can you determine that?
 
steph7 said:
I already split it apart, I understand how to do the arithmetic part the pi, 2pi and so on. But is the sum for the geometric part the a, a^2... just a? I’m using the formula.
Click to expand...
Can you show how you used the formula to get a? Formulas can be good, but you need to think; and it doesn't make a lot of sense that the sum of a lot of positive numbers would equal the first of them, so clearly something is wrong in either the formula or your use of it.
 
I made a mistake so I said a1=a, and r=a. S50= a/(1-a). The formula is a/(1-r). Am I using it wrong? ........edited ...those parentheses () are important.
 
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steph7 said:
I made a mistake so I said a1=a, and r=a. S50= a/(1-a). The formula is a/(1-r). Am I using it wrong?
Click to expand...
Yes... that equation sum for infinite terms - subject to condition r < 1.

The equation as quoted is incorrect - for limited term series..

Please locate the correct equation for limited terms (n = 50).
 
Yes, with n replaced by 50, of course.

Something you may want to do to convince yourself that you are right is to pick a simple value for a (say 2, or 1/2), and a smaller value for n (say, 5) and calculate the sum both directly and by your formula.
 
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