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We need to find a simple expression for the following infinite sums:
(i) 1-x+(x^2)/2! - (x^3)/3! +....
(ii) (x^2)/2 - (x^3)/3x2 + (x^4)/4x3 - (x^5)/5x4 +... for modulus of x<1
The hint for the second one is to differentiate. Still not sure how to go about these. We need to write them as functions apparently, not using sum notation.
(i) 1-x+(x^2)/2! - (x^3)/3! +....
(ii) (x^2)/2 - (x^3)/3x2 + (x^4)/4x3 - (x^5)/5x4 +... for modulus of x<1
The hint for the second one is to differentiate. Still not sure how to go about these. We need to write them as functions apparently, not using sum notation.
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#2
(Original post by pineapplechemist)
We need to find a simple expression for the following infinite sums:
(i) 1-x+(x^2)/2! - (x^3)/3! +....
(ii) (x^2)/2 - (x^3)/3x2 + (x^4)/4x3 - (x^5)/5x4 +... for modulus of x<1
The hint for the second one is to differentiate. Still not sure how to go about these. We need to write them as functions apparently, not using sum notation.
We need to find a simple expression for the following infinite sums:
(i) 1-x+(x^2)/2! - (x^3)/3! +....
(ii) (x^2)/2 - (x^3)/3x2 + (x^4)/4x3 - (x^5)/5x4 +... for modulus of x<1
The hint for the second one is to differentiate. Still not sure how to go about these. We need to write them as functions apparently, not using sum notation.
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#3
(Original post by pineapplechemist)
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The first is not that dissimiliar to a well known series - can you adapt it?
The second, if you differentiate it, is a standard series. So, do that, work out the function, and integrate the function to get the function for your original series.
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#5
(Original post by pineapplechemist)
We need to find a simple expression for the following infinite sums:
(i) 1-x+(x^2)/2! - (x^3)/3! +....
(ii) (x^2)/2 - (x^3)/3x2 + (x^4)/4x3 - (x^5)/5x4 +... for modulus of x<1
The hint for the second one is to differentiate. Still not sure how to go about these. We need to write them as functions apparently, not using sum notation.
We need to find a simple expression for the following infinite sums:
(i) 1-x+(x^2)/2! - (x^3)/3! +....
(ii) (x^2)/2 - (x^3)/3x2 + (x^4)/4x3 - (x^5)/5x4 +... for modulus of x<1
The hint for the second one is to differentiate. Still not sure how to go about these. We need to write them as functions apparently, not using sum notation.
Grouping
i.e the second group with pointwise differentiation
which you can integrate easily
Similarly for the first group but first take out x as factor before the differentiation
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