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Mathematics
Mathematics
Problem
Let
S
S
S
be the sum of the first 9 terms of the series :
{
x
+
k
a
}
+
{
x
2
+
(
k
+
2
)
a
}
+
{
x
3
+
(
k
+
4
)
a
}
+
{
x
4
+
(
k
+
6
)
a
}
+
…
\{x + ka\} + \{x^2 + (k + 2)a\} + \{x^3 + (k + 4)a\} + \{x^4 + (k + 6)a\} + \dots
{
x
+
k
a
}
+
{
x
2
+
(
k
+
2
)
a
}
+
{
x
3
+
(
k
+
4
)
a
}
+
{
x
4
+
(
k
+
6
)
a
}
+
…
where
a
≠
0
a \neq 0
a
=
0
and
x
≠
1
x \neq 1
x
=
1
. If
S
=
x
10
−
x
+
45
a
(
x
−
1
)
x
−
1
S = \frac{x^{10} - x + 45a(x - 1)}{x - 1}
S
=
x
−
1
x
10
−
x
+
45
a
(
x
−
1
)
, then
k
k
k
is equal to (a)
−
5
-5
−
5
(b)
1
1
1
(c)
−
3
-3
−
3
(d)
3
3
3
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