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| PAGE: 606 | SET: Exercises | PROBLEM: 111 |
(a).
At the beggining the budget of the government is 
billion per year.
After 
year it decreases by 
, which is same being multiplied by 
.
which is 
less than .
After 
years it again decreases by which is same being multiplied by 
.
which is less than 
.
After 
years, the amount budgetted is 
.
(b).
The budget of first 
is calculated by using the formula 
.
Where 
is number of years.
If 
, then 
.
If 
, then 
.
If 
, then 
.
If 
, then 
.
(c).
Observe the sequence:
The sequence is clearly decreasing and it is always positive meaning that it is bounded below by 
.
According to bounded monotonic sequences, if the sequence 
is bounded and monotonic, then it converges.
Therefore the sequence converges.
Further the limit of the sequence is 
.
The sequence converges and the limit is 
.
(a) Formula for the sequence is .
(b)
If 
, then 
.
If 
, then 
.
If 
, then 
.
If 
, then 
.
(c) The sequence converges and the limit is .
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