Thread: Constant of a series from Integration

When integrating a series, the constant from the integration is evaluated as part of the summation or is it as a constant "outside" of the whole summation?

Say I have

Then is the result equals to this: ?

Or is the result equals to this: ?

Thanks!

Either way is correct.

The C in your second equation equals the sum of C's in your first equation.

But how would it be the same?

In the first one, if say after some working, I found out that C=5. Then there is a summation of 5 for infinity times(which results in infinity) and then plus the summation of Xn.
But in the second one, if C=5, it would just be the summation of Xn and then plus 5, wouldn't it?

Originally Posted by xEnOn

But how would it be the same?

In the first one, if say after some working, I found out that C=5. Then there is a summation of 5 for infinity times(which results in infinity) and then plus the summation of Xn.
But in the second one, if C=5, it would just be the summation of Xn and then plus 5, wouldn't it?

The C's in your first equation probably form a convergent sequence, whose sum is the C in your second equation.

The sum of constants is still a constant...