Prove the formula for all natural numbers n.
?

?
List the steps involved.

What will be an ideal response?


Step 1: We must verify that is true. However, is just the statement that , which is true.

Step 2: Assuming that is true, we must prove that is true. Let's examine and .

.

is obtained by substituting + 1 for n in .

.

If we add to the both sides of the equation for , we'll get the equation for .

Since equation for follows from equation for , we have demonstrated that .


Mathematics

You might also like to view...

Determine whether the inequality is a true statement.- 2 ? - 18

A. True B. False

Mathematics

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such.f(x) = x + 6

A. D = (-?, ?), R = (-?, ?)

B. D = (-?, ?), R = (-?, ?)

C. D = (-?, ?), R = (-?, ?)

D. D = (-?, ?), R = (-?, ?)

Mathematics

Graph the rational function.f(x) = 

A.

B.

C.

D.

Mathematics

Write the terms for the partial fraction decomposition of the rational function. Do not solve for the constants.

A.  +  
B.   +   +  +  +  
C.   +   +   + 
D.  +   +  

Mathematics