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Byju's Answer
Standard XII
Mathematics
Dot Product of Two Vectors
P.T that 1 ×...
Question
P.T that
(
1
×
2
×
5
)
+
(
2
×
5
×
7
)
+
(
3
×
4
×
9
)
+
.
.
.
.
.
.
i
s
n
(
n
+
1
)
(
n
+
2
)
(
3
n
+
7
)
6
.
Open in App
Solution
Given
(
1
×
2
×
5
)
+
(
2
×
5
×
7
)
+
(
3
×
4
×
9
)
+
.
.
.
.
.
.
∞
=
n
(
n
+
1
)
(
n
+
2
)
(
3
n
+
7
)
6
take
n
=
1
LHS:
=
1
×
2
×
5
=
10
RHS:
=
1
(
1
+
1
)
(
1
+
2
)
(
3
(
1
)
+
7
)
6
=
6
×
10
6
=
10
LHS=RHS
take
n
=
k
LHS:
(
1
×
2
×
5
)
+
(
2
×
5
×
7
)
+
(
3
×
4
×
9
)
+
.
.
.
.
.
.
∞
RHS:
=
k
(
k
+
1
)
(
k
+
2
)
(
3
k
+
7
)
6
LHS=RHS
Now to prove that
n
=
k
+
1
is also true
LHS:
(
1
×
2
×
5
)
+
(
2
×
5
×
7
)
+
(
3
×
4
×
9
)
+
.
.
.
.
.
.
∞
RHS:
=
(
k
+
1
)
(
(
k
+
1
)
+
1
)
(
(
k
+
1
)
+
2
)
(
3
(
k
+
1
)
+
7
)
6
=
(
k
+
1
)
(
k
+
2
)
(
(
k
+
3
)
(
3
k
+
10
)
6
=
n
(
n
+
1
)
(
n
+
2
)
(
3
n
+
7
)
6
where
n
=
k
+
1
Therefore
(
1
×
2
×
5
)
+
(
2
×
5
×
7
)
+
(
3
×
4
×
9
)
+
.
.
.
.
.
.
∞
=
n
(
n
+
1
)
(
n
+
2
)
(
3
n
+
7
)
6
Hence proved by induction
Suggest Corrections
0
Similar questions
Q.
Prove that
(
1
×
2
×
5
)
+
(
2
×
3
×
7
)
+
(
3
×
4
×
9
)
+
.
.
.
.
.
is
n
(
n
+
1
)
(
n
+
2
)
(
3
n
+
7
)
6
Q.
Prove that :
(
1
×
2
×
5
)
+
(
2
×
3
×
7
)
+
(
3
×
4
×
9
)
+
.
.
.
.
.
(
n
t
e
r
m
s
)
is equal to
n
(
n
+
1
)
(
n
+
2
)
(
3
n
+
7
)
6
.
Q.
Study the following number line and answer the questions that follow.
2 5 9 1 7 2 5 1 9 7 3 9 5 2 4 6 8 1 9 7 5 2 7 3 1 9 7 8 5 2 6 5 4 1 9 7 8 2 0 1 0 9 7 8 5 1 9 7 3 5 1 6 9 7 2 1 7 3 7 9 5 1
How many times is number 9 preceded by 1 and succeeded by 7 which is not followed by 5 ?
Q.
Study the following number line and answer the questions that follow.
2 5 9 1 7 2 5 1 9 7 3 9 5 2 4 6 8 1 9 7 5 2 7 3 1 9 7 8 5 2 6 5 4 1 9 7 8 2 0 1 0 9 7 8 5 1 9 7 3 5 1 6 9 7 2 1 7 3 7 9 5 1
How many times is number '3' preceded by number '7' and not followed by an even number?
Q.
Prove that :
1
√
2
+
1
+
1
√
3
+
√
2
+
1
√
4
+
√
3
+
1
√
5
+
√
4
+
1
√
6
+
√
5
+
1
√
7
+
√
6
+
1
√
8
+
√
7
+
1
√
9
+
√
8
=
2
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