A number theory problem by Paola Ramírez

Number Theory Level 2

Compute:

99 − 97 + 95 − 93 + . . . + 3 − 1 99-97+95-93+...+3-1


The answer is 50.

Paola Ramírez by Paola Ramírez , 24, Mexico

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1 solution

Áron Bán-Szabó
Jul 15, 2017

99 − 97 + 95 − 93 + 91 − 89 + 87 − 85 + ⋯ + 7 − 5 + 3 − 1 = 2 + 2 + 2 + 2 + ⋯ + 2 + 2 ⏟ Number of 2 = 25 = 25 ∗ 2 = 50 \color{#D61F06} 99-97 \color{#333333} + \color{#3D99F6} 95-93 \color{#333333} + \color{#D61F06} 91-89 \color{#333333} + \color{#3D99F6} 87-85 \color{#333333} + \dots + \color{#D61F06} 7-5 \color{#333333} + \color{#3D99F6} 3-1 \color{#333333} = \underbrace{\color{#D61F06} 2 \color{#333333} + \color{#3D99F6} 2 + \color{#D61F06} 2 \color{#333333} + \color{#3D99F6} 2 \color{#333333} + \dots + \color{#D61F06} 2 \color{#333333} + \color{#3D99F6} 2 \color{#333333}}_{\text{Number of 2} \ = 25} = 25*2=\boxed{50}

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