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Byju's Answer
Standard XII
Mathematics
Algebra of Limits
Find the valu...
Question
Find the value of:
(
a
m
a
−
n
)
m
−
n
×
(
a
n
a
−
1
)
n
−
1
×
(
a
1
a
−
m
)
1
−
m
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Solution
We have
(
a
m
a
−
n
)
m
−
n
×
(
a
n
a
−
1
)
n
−
1
×
(
a
1
a
−
m
)
1
−
m
By using law
a
m
a
n
=
a
m
−
n
=
(
a
m
+
n
)
m
−
n
×
(
a
n
+
1
)
n
−
1
×
(
a
m
+
1
)
1
−
m
=
a
m
2
−
n
2
×
a
n
2
−
1
2
×
a
1
2
−
m
2
By using law
a
m
×
a
n
=
a
m
+
n
=
a
m
2
−
n
2
+
n
2
−
1
+
1
−
m
2
=
a
0
=
1
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Similar questions
Q.
(
a
m
a
−
n
)
m
−
n
×
(
a
n
a
−
1
)
n
−
1
×
(
a
1
a
−
m
)
1
−
m
=
Q.
Evaluate
(
a
m
a
−
n
)
m
−
n
×
(
a
n
a
−
l
)
n
−
l
×
(
a
l
a
−
m
)
l
−
m
Q.
If
(
1
+
x
)
n
=
n
∑
r
=
0
a
r
x
r
.
Then
(
1
+
a
1
a
0
)
(
1
+
a
2
a
1
)
…
(
1
+
a
n
a
n
−
1
)
is equal to
Q.
If
a
1
is the greatest value of
f
(
x
)
=
1
2
+
[
s
i
n
x
]
and
a
n
+
1
=
(
−
1
)
n
+
2
n
+
1
+
a
n
Then
l
i
m
n
→
∞
a
n
=
_________
Q.
Find the next five terms of each of the following sequences given by:
(i) a
1
= 1, a
n
= a
n−1
+2, n ≥ 2
(ii) a
1
= a
2
= 2, a
n
= a
n−1
− 3, n > 2
(iii)
a
1
=
-
1
,
a
n
=
a
n
-
1
n
,
n
≥
2
(iv) a
1
= 4, a
n
= 4a
n−1
+ 3, n > 1.