Matematika - Universityku

Tentukan nilai dari
$(1 - frac{ {2}^{2} }{100} ) times (1 - frac{ {3}^{2} }{100} ) times (1 - frac{ {4}^{2} }{100} ) times ... times (1 - frac{ {99}^{2} }{100} ) \$
Plis jawab

Matematika

Penjelasan dengan langkah-langkah:

$= (1 - frac{ {2}^{2} }{100} ) times (1 - frac{ {3}^{2} }{100} ) times (1 - frac{ {4}^{2} }{100} ) times ... times (1 - frac{ {99}^{2} }{100} )$

$= (1 - frac{ {2}^{2} }{100} )(1 - frac{ {3}^{2} }{100} ) times ... times (1 - frac{ {10}^{2} }{100} ) times ... times (1 - frac{ {99}^{2} }{100} )$

$= (1 - frac{ {2}^{2} }{100} )(1 - frac{ {3}^{2} }{100} ) times ... times (1 - frac{100}{100} ) times ... times (1 - frac{ {99}^{2} }{100} )$

$= (1 - frac{ {2}^{2} }{100} )(1 - frac{ {3}^{2} }{100} ) times ... times (1 - 1) times ... times (1 - frac{ {99}^{2} }{100} )$

$= (1 - frac{ {2}^{2} }{100} )(1 - frac{ {3}^{2} }{100} ) times ... times0 times ... times (1 - frac{ {99}^{2} }{100} )$

$= 0$