Prove the formula for all natural numbers n.
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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 
.
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Solve the problem by estimating.The population of Capital City is 7,695,831 and the population of Spring City is 4,032,652. Round each population to the nearest hundred-thousand to estimate how much larger Capital City is than Spring City.
A. 3,600,000 B. 3,800,000 C. 3,700,000 D. 3,663,000
Perform the indicated operation and simplify.
+ 
A. 
B. 
C. 
D. 
If necessary, write the equation in the standard form ax2 + bx + c = 0. Then identify the values of a, b, and c. Do not actually solve the equation.(x - 5)(x - 6) = 0
A. a = 1, b = 0, c = 30 B. a = 0, b = 11, c = 30 C. a = 1, b = -11, c = 30 D. a = 1, b = -11, c = -30
Simplify the fraction.
If the fraction is undefined, answer undefined.
What will be an ideal response?