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Byju's Answer
Standard XII
Mathematics
Sigma n2
Let the sum o...
Question
Let the sum of
n
terms of the series,
5
+
55
+
555
+
.
.
.
.
.
be
S
n
=
50
81
(
k
n
−
1
)
−
5
9
n
. Find k ?
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Solution
Let
S
n
=
5
+
55
+
555
+
.
.
.
.
.
.
.
.
.
.
.
.
.
n
terms
=
5
{
1
+
11
+
111
+
.
.
.
.
n
t
e
r
m
s
}
=
5
9
{
9
+
99
+
999
+
.
.
.
.
.
n
t
e
r
m
s
}
=
5
9
{
(
10
−
1
)
+
(
100
−
1
)
+
(
1000
−
1
)
+
.
.
.
.
.
n
t
e
r
m
s
}
=
5
9
{
(
10
+
100
+
1000
+
.
.
.
.
.
n
t
e
r
m
s
)
−
(
1
+
1
+
1
+
.
.
.
.
.
.
n
t
e
r
m
s
)
}
=
5
9
[
10
(
10
n
−
1
)
10
−
1
−
n
]
=
50
81
(
10
n
−
1
)
−
5
9
n
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