Question

F (k)= 5^k Найти F (k+2) - F (k+1)

Answer 1

F(k)=5^k
F(k+2)-F(k+1)=5^(k+2)-5^(k+1)=

5^((k+1)+1)-5^(k+1)=

5*5^(k+1)-5^(k+1)=5^(k+1) •(5-1)=

4*5^(k+1)

Answer 2

To find the value of F(k+2) - F(k+1) for the function F(k) = 5^k, we first need to evaluate F(k+2) and F(k+1) separately and then subtract them.

Step 1: Find F(k+2) Replace k with (k+2) in the function F(k) = 5^k: F(k+2) = 5^(k+2)

Step 2: Find F(k+1) Replace k with (k+1) in the function F(k) = 5^k: F(k+1) = 5^(k+1)

Step 3: Calculate the difference Now, subtract F(k+1) from F(k+2): F(k+2) - F(k+1) = 5^(k+2) - 5^(k+1)

To simplify the expression, we can factor out 5^(k+1): F(k+2) - F(k+1) = 5^(k+1) * (5 - 1)

Finally, simplify the expression: F(k+2) - F(k+1) = 5^(k+1) * 4

So, the expression for F(k+2) - F(k+1) for the function F(k) = 5^k is 4 * 5^(k+1).