MathDB
Problems
Contests
National and Regional Contests
India Contests
India IOQM
2020-21 IOQM India
18
IOQM 2021 P18
IOQM 2021 P18
Source:
January 17, 2021
Problem Statement
If
∑
k
=
1
40
(
1
+
1
k
2
+
1
(
k
+
1
)
2
)
=
a
+
b
c
\sum_{k=1}^{40} \left( \sqrt{1 + \frac{1}{k^{2}} + \frac{1}{(k + 1)^{2}}}\right) = a + \frac {b}{c}
k
=
1
∑
40
(
1
+
k
2
1
+
(
k
+
1
)
2
1
)
=
a
+
c
b
where
a
,
b
,
c
∈
N
,
b
<
c
,
g
c
d
(
b
,
c
)
=
1
,
a, b, c \in \mathbb{N}, b < c, gcd(b,c) =1 ,
a
,
b
,
c
∈
N
,
b
<
c
,
g
c
d
(
b
,
c
)
=
1
,
then what is the value of
a
+
b
?
a+ b ?
a
+
b
?
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