sum the series 5 + 55 +555..... upto n term
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Answered by
6
Answer:
ANSWER
Let S
n
=5+55+555+... to n terms.
Then,
s
n
=5(1+11+111+... to n terms)
⇒s
n
=
5
9
(9+99+999+... to n terms)
⇒S
n
=
9
5
{(10−1)+(10
2
−1)+(10
3
−1)+...+(10
n
−1)}
⇒S
n
=
9
5
{(10+10
2
+10
3
+...+10
n
)−n}
⇒S
n
=
9
5
{10(
10−1
10
n
−1
)−n}
⇒S
n
=
9
5
{
9
10
(10
n
−1)−n}=
81
5
(10
n+1
−9n−10).
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