Let S_n&=1-2+3-4+… & +(-1)^n-1n. Here n=1, 2, …. Then S_17+S_33+S_50 equals:

1968 AMC 12 Problem 27

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27.

Let

\begin{aligned} S_n&=1-2+3-4+\cdots\\ &\quad+(-1)^{n-1}n. \end{aligned}

Here

n=1,

2,

\ldots.

Then

S_{17}+S_{33}+S_{50}

equals:

0

1

2

-1

-2

Pair terms as

(1-2)+(3-4)+\cdots

For even

n,

S_n=-\frac{n}{2};

for odd

n,

S_n=\frac{n+1}{2}

Pairing gives

S_n=-\frac{n}{2}

for even

n

and

S_n=\frac{n+1}{2}

for odd

n.

Hence

S_{17}=9,

S_{33}=17,

S_{50}=-25,

and their sum is

1.

Therefore, the correct answer is B.