Prove the formula for all natural numbers n.
?
?
List the steps involved.
What will be an ideal response?
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 k + 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 
.
You might also like to view...
Solve the problem.In a certain location, the highest temperature recorded was 101°F. The lowest temperature recorded was 136 degrees less than the highest. What was the lowest temperature?
A. -35°F B. 0°F C. -138°F D. 35°F
Find the Taylor polynomial of order 3 generated by f at a.f(x) = 
, a = 1
A. P3(x) = 
- 
+ 
- 
B. P3(x) = 
- 
+ 
- 
C. P3(x) = 
- 
+ 
- 
D. P3(x) = 
- 
+ 
- 
Apply Green's Theorem to evaluate the integral.
(y2 + 6) dx + (x2 + 1) dyC: The triangle bounded by x = 0, x + y = 2, y = 0
A. 
B. 32
C. -24
D. 0
Solve the polynomial equation graphically or numerically. Round to the nearest hundredth if necessary.6x3 + 25x2 + 12x - 7 = 0
A. - 1, - 
, 
B. - 1, 
, 
C. - 
, - 
, 
D. 
, 
, - 