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Byju's Answer
Standard XII
Mathematics
Index of (r+1)th Term from End When Counted from Beginning
State whether...
Question
State whether the statement is true/false
50
n
−
49
n
−
1
is divisible by
49
3
for all positive integer
n
.
A
True
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B
False
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Solution
The correct option is
B
False
Let us write
50
n
as
(
1
+
49
)
n
Using Binomial expansion
(
1
+
49
)
n
=
1
+
n
C
1
(
49
)
+
n
C
2
(
49
)
2
+
n
C
3
(
49
)
3
+
.
.
.
.
⟹
50
n
=
1
+
49
n
+
n
(
n
−
1
)
2
(
49
)
2
+
n
(
n
−
1
)
(
n
−
2
)
6
(
49
)
3
+
.
.
.
.
⟹
50
n
−
49
n
−
1
=
n
(
n
−
1
)
2
(
49
)
2
+
n
(
n
−
1
)
(
n
−
2
)
6
(
49
)
3
+
.
.
.
.
So the Given expression is not divisible by
49
3
Suggest Corrections
0
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Standard XII Mathematics
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