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Byju's Answer
Standard X
Mathematics
Sum of n Terms
Find the sum ...
Question
Find the sum to n terms
(
7
+
77
+
777
+
.
.
.
.
.
n
terms)
Open in App
Solution
Let s be the sum of n terms of sumes,
(7+77+777+....n terms)
∴
7+77+777+....n terms
=7(1+11+111+....n terms )
=
7
9
(
9
+
99
+
999
+
.
.
.
.
n
t
e
r
m
s
)
=
7
9
[
(
10
−
1
)
+
(
10
2
−
1
)
(
10
3
−
1
)
+
.
.
.
.
n
t
e
r
m
s
]
=
7
9
[
(
10
+
10
2
+
10
3
.
.
.
.
t
o
n
t
r
e
m
s
)
(
1
+
1
+
.
.
.
n
t
e
r
m
s
)
]
=
7
9
[
10
(
10
n
−
1
)
10
−
1
−
n
]
=
7
9
[
10
9
(
10
n
−
1
)
−
n
]
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