Calculate (0.11)^3 using binomial approximation
Answers
Answer:
example
Step-by-step explanation:
Original question: Use binomial theorem to find
(
1.02
)
8
Consider the binomial theorem:
(
a
+
b
)
n
=
(
n
0
)
a
n
b
0
+
(
n
1
)
a
n
−
1
b
1
+
...
+
(
n
n
−
1
)
a
1
b
n
−
1
+
(
n
n
)
a
0
b
n
where
n
is a positive integer and
(
x
y
)
is
x
choose
y
.
Since the binomial theorem only works on values in the form of a binomial: Consider that
1.02
=
1
+
0.02
=
1
+
1
50
So, by substituting
1.02
=
1
+
1
50
, we get:
(
1
+
1
50
)
8
By applying the binomial theorem, we get:
=
(
8
0
)
+
(
8
1
)
(
1
50
)
+
(
8
2
)
(
1
50
)
2
+
(
8
3
)
(
1
50
)
3
+
(
8
4
)
(
1
50
)
4
+
(
8
5
)
(
1
50
)
5
+
(
8
6
)
(
1
50
)
6
+
(
8
7
)
(
1
50
)
7
+
(
8
8
)
(
1
50
)
8
=
1
+
8
50
+
28
50
2
+
56
50
3
+
70
50
4
+
56
50
5
+
28
50
6
+
8
50
7
+
1
50
8
=
45767944570401
39062600000000
≈
1.17166
rounded to 5 decimal places
We can confirm this result:
(
1.02
)
8
≈
1.17166
rounded to 5 decimal places
Step-by-step explanation:
hey dear refer to the attachment for the answer
answer is .001331 in the picture
I hope I have utilised ur given 50 points
Plz mark it brainliest and plz don't spam
