simplify first three terms in the
expansion of the following (5-3x) ^-1/3
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Answer:
Whatever be value of n, negative integer or positive or negative fraction,
(1+x)
n
=1+
1!
n
x+
2!
n(n−1)
x
2
+
3!
n(n−1)(n−2)
x
3
+...+...+
r!
n(n−1)(n−2)...(n−r+1)
x
r
+...
where, ∣x∣<1 i.e. −1<x<1.
Now,
Expanding the two binomials as far as the term containing x
2
using above formula, we have
=(1+
2
3
x−
8
9
x
2
−.)(1+
3
2
x+
9
8
x
2
+..)
=1+x(
2
3
+
3
2
)+x
2
[−
8
9
+(
2
3
⋅
3
2
)+
9
8
]+.
=1+
6
13
x+
72
55
x
2
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