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Byju's Answer
Standard XII
Mathematics
Vn Method
If ∑ k =13601...
Question
If
360
∑
k
=
1
(
1
k
√
k
+
1
+
(
k
+
1
)
√
k
)
=
a
,
then the value of
19
a
is
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Solution
Let
T
k
=
1
√
k
√
k
+
1
[
√
k
+
√
k
+
1
]
=
√
k
+
1
−
√
k
√
k
√
k
+
1
=
1
√
k
−
1
√
k
+
1
∴
S
=
360
∑
k
=
1
(
1
√
k
−
1
√
k
+
1
)
=
1
−
1
√
361
=
1
−
1
19
=
18
19
=
a
∴
19
a
=
18
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1
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Standard XII Mathematics
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