simplyfy 5^n+3 -6× 5^n+1 upon 9×5^n-5^n ×2^2
Answers
Answered by
4
Answer:
3
(
n
+
1
)
!
5
n
!
=
3
(
n
+
1
)
5
Explanation:
The factorial of any integer
n
is given by
n
!
=
n
(
n
−
1
)
(
n
−
2
)
(
n
−
3
)
...
(
3
)
(
2
)
(
1
)
Therefore, the factorial of
n
+
1
would be
(
n
+
1
)
!
=
(
n
+
1
)
(
n
)
(
n
−
1
)
(
n
−
2
)
(
n
−
3
)
...
(
3
)
(
2
)
(
1
)
Using these two expression in our original question,
3
(
n
+
1
)
!
5
n
!
=
3
(
n
+
1
)
(
n
)
(
n
−
1
)
(
n
−
2
)
...
(
3
)
(
2
)
(
1
)
5
(
n
)
(
n
−
1
)
(
n
−
2
)
...
(
3
)
(
2
)
(
1
)
All terms in the denominator except
5
are cancelled out by corresponding terms in the numerator. Therefore, you finally get
3
(
n
+
1
)
!
5
n
!
=
3
(
n
+
1
)
5
Answered by
4
Answer:
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