Calculate

Algebra Level 2

0 − 1 + 2 − 3 + 4 − 5 + 6 − 7 + 8 + ⋯ + 96 0-1+2-3+4-5+6-7+8+\cdots +96

Without using calculator find the above sum.


The answer is 48.

Lakshya Khilwani by Lakshya Khilwani , 17, India

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1 solution

Chew-Seong Cheong
Sep 23, 2018

S = 0 − 1 + 2 ⏞ = 1 − 3 + 4 ⏞ = 1 − 5 + 6 ⏞ = 1 − ⋯ − 95 + 96 ⏞ = 1 ⏟ Number of 1s=48 = 48 \begin{aligned} S & = 0\ \underbrace{\overbrace{\color{#3D99F6} - 1+2}^{=1}\ \overbrace{\color{#D61F06} - 3+4}^{=1}\ \overbrace{\color{#3D99F6} - 5+6}^{=1}\ - \cdots\ \overbrace{\color{#D61F06} -95 + 96} ^{=1}}_{\text{Number of 1s=48}} \\ & = \boxed{48} \end{aligned}

6 Helpful 0 Interesting 1 Brilliant 0 Confused

I didn't look at the question from that angle

Ömer Ertürk - 5 months, 1 week ago

and nice solve

Ömer Ertürk - 5 months, 1 week ago

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Glad that you like it.

Chew-Seong Cheong - 5 months, 1 week ago

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