IB Mathematics Analysis and Approaches Quiz
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NUMBER AND ALGEBRA
Question 1
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Which of the following mathematical propositions is most appropriately proven using proof by contradiction?
A
For
n
∈
Z
+
n \in \mathbb{Z}^+
n
∈
Z
+
,
∑
i
=
1
n
i
2
=
n
(
n
+
1
)
(
2
n
+
1
)
6
\sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6}
∑
i
=
1
n
i
2
=
6
n
(
n
+
1
)
(
2
n
+
1
)
.
B
The sum of a rational number and an irrational number is irrational.
C
For any
n
∈
Z
+
n \in \mathbb{Z}^+
n
∈
Z
+
, the
n
n
n
-th derivative of
e
2
x
e^{2x}
e
2
x
is
2
n
e
2
x
2^n e^{2x}
2
n
e
2
x
.
D
The sum of the first
n
n
n
terms of a geometric series is
S
n
=
a
(
r
n
−
1
)
r
−
1
S_n = \frac{a(r^n-1)}{r-1}
S
n
=
r
−
1
a
(
r
n
−
1
)
.
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