Base case: For
, the left side is 2 and the right is
, so the base case holds.
Induction hypothesis: Assume the statement is true for
, that is

We want to show that this implies truth for
, that

The first
terms on the left reduce according to the assumption above, and we can simplify the
-th term a bit:


so the statement is true for all
.
Answer: 360
Step-by-step explanation: Anytime it asks for the exterior sum it will always be 360
Answer:
25 e books
Step-by-step explanation:
because you multiply the money by 5 which gets you 40. Then you multiply the number of e books by 5 and you get 25.
9514 1404 393
Answer:
5⬥ = ▼
Step-by-step explanation:
Let's use T, D, C, S to represent the numbers of triangles, diamonds, circles, and squares on each balance. We are given ...
T +D = C . . . . [eq1]
T = D +S . . . . [eq2]
2C = 3S . . . . [eq3]
Using [eq2] to substitute for T in [eq1], we have ...
(D +S) + D = C
Substituting for C in [eq3] gives ...
2(2D +S) = 3S
4D +2S = 3S . . . . . eliminate parentheses
4D = S . . . . . . . . . . subtract 2S
Substituting this into [eq2], we have ...
T = D +4D
T = 5D . . . . . . . . . collect terms. This answers the question.
5⬥ are needed to balance the scale
_____
<em>Additional comment</em>
We cannot tell the intent of "Each letter represents a digit. The sum of every three consecutive digits is 19." No letters are shown.
The answer is C 9x^2+12x+4-9y^2