Use mathematical induction to prove the statement is true for all positive integers n.11 + 22 + 33 + . . . + 11n = 
What will be an ideal response?
Answers may vary. Possible answer:
First, we show the statement is true when n = 1.
For n = 1, we get 11 = 
Since 
= 
= 11, P1 is true and the first condition for the principle of induction is satisfied.
Next, we assume the statement holds for some unspecified natural number k. That is,
Pk: 
is assumed true.
On the basis of the assumption that Pk is true, we need to show that Pk+1 is true.
Pk+1: 
So we assume that 
is true and add the next term, 
to both sides of the equation.
11 + 22 + 33 + ... + 11k + 11(k + 1) = 
+ 11(k + 1)
11 + 22 + 33 + ... + 11k + 11(k + 1) = 11
11 + 22 + 33 + ... + 11k + 11(k + 1) = 
The last equation says that Pk+1 is true if Pk is assumed to be true. Therefore, by the principle of mathematical induction, the statement 11 + 22 + 33 + ... + 11n = 
is true for all natural numbers n.
You might also like to view...
Use the integral test to determine whether the following series is convergent or divergent.
?
What will be an ideal response?
Graph the function.f(x) = 
A. 
B. 
C. 
D. 
Find the exact value of the expression if ? = 45°. Do not use a calculator.f(?) = cos ?Find 7f(?).
A. - 
B. 
C. - 
D. 
Differentiate.y = 
A. 
B. 
C. 
D. 