Prove that

where is a nonnegative integer and is any real number, which is not a negative integer.

[Hint: Use the method of mathematical induction and integration by parts.]

I do not understand how to proceed with induction?

- October 8th 2013, 08:27 PMvidomagruUse Mathematical Induction and Integration by Parts to prove integral
Prove that

where is a nonnegative integer and is any real number, which is not a negative integer.

[*Hint*: Use the method of mathematical induction and integration by parts.]

I do not understand how to proceed with induction? - October 8th 2013, 08:38 PMSlipEternalRe: Use Mathematical Induction and Integration by Parts to prove integral
Is a variable that depends on ? What is the relationship?[/tex]

- October 8th 2013, 08:40 PMvidomagruRe: Use Mathematical Induction and Integration by Parts to prove integral
- October 8th 2013, 08:43 PMSlipEternalRe: Use Mathematical Induction and Integration by Parts to prove integral
- October 8th 2013, 08:53 PMibduttRe: Use Mathematical Induction and Integration by Parts to prove integral
That way we just cannot get what appears in the denominator on the RHS. it looks as if there is something missing.

- October 9th 2013, 01:22 AMtopsquarkRe: Use Mathematical Induction and Integration by Parts to prove integral
- October 9th 2013, 07:17 AMSlipEternalRe: Use Mathematical Induction and Integration by Parts to prove integral
Ok, I get it now. The dt was throwing me. With dx, it actually seems fairly trivial, so I may be missing something.

Base case: n = 0

So, it satisfies the base case. Suppose it is true for all nonnegative integers less than . I want to show it is true for .

The integration by parts is very straightforward: .

Now, we have:

The first term is zero at both 1 and 0. For the second term, since and is a nonnegative integer less than , so by the induction assumption, we can apply the hypothesis. - October 9th 2013, 06:46 PMvidomagruRe: Use Mathematical Induction and Integration by Parts to prove integral
- October 15th 2013, 01:34 PMvidomagruRe: Use Mathematical Induction and Integration by Parts to prove integral
So based on your help, this is my proof. Does this seem accurate?

**Problem:**

where is a nonnegative integer and is any real number, which is not a negative integer.

[*Hint*: Use the method of mathematical induction and integration by parts.]

**Proof:**We will prove this by Mathematical Induction.

We need to show that it holds for n=0. Now,

and this simplifies to:

.

Hence it holds for n=0. Now, suppose that it is true for , we need to show that it holds for .

First, evaluate the integral using integration by parts. Let . So now, we have:

.

Now, = 0 + 0 = 0.

Now by our assumption we have , so now consider .

.

**Where do I go about applying the hypothesis of n = k?** - October 15th 2013, 04:21 PMSlipEternalRe: Use Mathematical Induction and Integration by Parts to prove integral
- October 15th 2013, 06:24 PMvidomagruRe: Use Mathematical Induction and Integration by Parts to prove integral
- October 15th 2013, 09:21 PMvidomagruRe: Use Mathematical Induction and Integration by Parts to prove integral
- October 15th 2013, 09:41 PMSlipEternalRe: Use Mathematical Induction and Integration by Parts to prove integral