I'm partial to solving with generating functions. Let
Multiply both sides of the recurrence by and sum over all .
Shift the indices and factor out powers of as needed so that each series starts at the same index and power of .
Now we can write each series in terms of the generating function . Pull out the first few terms so that each series starts at the same index .
Solve for :
Splitting into partial fractions gives
which we can write as geometric series,
which tells us
# # #
Just to illustrate another method you could consider, you can write the second recurrence in matrix form as
By substitution, you can show that
or
Then solving the recurrence is a matter of diagonalizing the coefficient matrix, raising to the power of , then multiplying by the column vector containing the initial values. The solution itself would be the entry in the first row of the resulting matrix.
Answer: 8
Step-by-step explanation:
Answer:
idek but I'll try solving it I'm hyu when I'm done
Answer:
Step-by-step explanation:
Given : You planned to work on a project for about 4 and a 1/2 hours today.
To Find :If you have been working on it for 1 and 3/4 hours, how much more time will it take?
Solution:
Total time to be spent on project today =
You have been working on it for hours =
Remaining time =
=
=
Hence it will take hours more .