Find the value of a0,A1 and A2.
Answers
Answer:
Step-by-step explanation:(1+x)
2n
=1+
2n
C
1
x+
2n
C
2
x
2
+....+
2n
C
2n
x
2n
or,
(1+x)
2n
=a
0
+a
1
x+a
2
x
2
+...+a
2n
x
2n
...(i)
Similarly,
(1−x)
2n
=a
0
−a
1
x+a
2
x
2
+...+a
2n
x
2n
....(ii)
As, a
0
=a
2n
, a
1
=a
2n−1
,...and so on. So, (i) and (ii) can be written as:
(1−x)
2n
=a
2n
−a
2n−1
x+a
2n−2
x
2
+...+a
0
x
2n
(1+x)
2n
=a
0
+a
1
x+a
2
x
2
+...+a
2n
x
2n
So, required answer is coefficient of x
2n
in (1+x)
2n
.(1−x)
2n
= coefficient of x
2n
in (1−x
2
)
2n
T
r+1
=
2n
C
r
(−x
2
)
r
=
2n
C
r
(−1)
r
(x)
2r
So, we need, r=n. Hence, the answer is (−1)
n
.a
n
For n−even, the answer is option A, i.e; a
n