- #1

transmini

- 81

- 1

$$\sum_{n=1}^\infty \frac{MK^{n-1}|t-t_0|^n}{n!} = \frac{M}{K}(e^{K(t-t_0)}-1)$$

I get most of the function, I just can't see where the ##-1## comes from. Could someone help show that?

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- Thread starter transmini
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- #1

transmini

- 81

- 1

$$\sum_{n=1}^\infty \frac{MK^{n-1}|t-t_0|^n}{n!} = \frac{M}{K}(e^{K(t-t_0)}-1)$$

I get most of the function, I just can't see where the ##-1## comes from. Could someone help show that?

- #2

- 9,568

- 774

$$\sum_{n=1}^\infty \frac{MK^{n-1}|t-t_0|^n}{n!} = \frac{M}{K}(e^{K(t-t_0)}-1)$$

I get most of the function, I just can't see where the ##-1## comes from. Could someone help show that?

The first term in the expansion of ##e^x## is ##1##, usually put in the sum with index ##0##. In your case the sum starts with ##n=1## so the constant term is missing on the left side. If you move the constant term from the right side to the left you will see it.

- #3

transmini

- 81

- 1

Oh, not sure how I missed that. That makes sense, thanksThe first term in the expansion of ##e^x## is ##1##, usually put in the sum with index ##0##. In your case the sum starts with ##n=1## so the constant term is missing on the left side. If you move the constant term from the right side to the left you will see it.

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