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Mathematics
Mathematics
Problem
Let
S
n
S_n
S
n
denote the sum of the first
n
n
n
odd natural numbers. a. (i) Express
S
n
S_n
S
n
using summation notation. b. (ii) Prove that
S
n
=
n
2
S_n=n^{2}
S
n
=
n
2
. c. (iii) Hence evaluate
∑
k
=
51
100
(
2
k
−
1
)
\displaystyle \sum_{k=51}^{100}(2k-1)
k
=
51
∑
100
(
2
k
−
1
)
without direct addition of terms.
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