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AIEEE 2004 Math Solved Paper
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© examsnet.com
Question : 11
Total: 68
Let
S
(
K
)
=
1
+
3
+
5
.
.
.
+
(
2
K
−
1
)
=
3
+
K
2
. Then which of the following is true
Principle of mathematical induction can be used to prove the formula
S
(
K
)
⇒
S
(
K
+
1
)
S
(
K
)
≠
S
(
K
+
1
)
S
(
1
)
is correct
Validate
Solution:
Given
S
(
K
)
=
1
+
3
+
5
.
.
.
+
(
2
K
−
1
)
=
3
+
K
2
When
k
=
1
,
S
(
1
)
:
1
=
3
+
1
L.H.S of
S
(
k
)
≠
R.H.S of
S
(
k
)
So
S
(
1
)
is not true.
As
S
(
1
)
is not true so principle of mathematical induction can not be used.
Now let
S
(
k
)
is true
∴
1
+
3
+
5
+
.
.
.
.
.
.
(
2
k
−
1
)
=
3
+
k
2
⇒
1
+
3
+
5
+
.
.
.
.
.
.
(
2
k
−
1
)
+
(
2
k
+
1
)
=
3
+
k
2
+
2
k
+
1
=
3
+
(
k
+
1
)
2
⇒
S
(
k
+
1
)
is true.
∴
S
(
k
)
⇒
S
(
k
+
1
)
© examsnet.com
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