c) C=(151515/161616 + 17^9/17^10)-(1500/1600 - 1616/1717)
=(15/16 + 1/17)-(15/16 - 16/17)
= 15/16 ( 1/17 + 16/17)
=15/16 . 1 = 15/16
bài c chỉ caàn rút gọn thôi nhé 151515/161616 = 15/16., 17^9/17^10 = 1/17, TƯƠNG TỰ NHÉ
c) \(C=\left(\dfrac{151515}{161616}+\dfrac{17^9}{17^{10}}\right)-\left(\dfrac{1500}{1600}-\dfrac{1616}{1717}\right)\)
\(=\left(\dfrac{15\times10101}{16\times10101}+\dfrac{17^9}{17^9.17}\right)-\left(\dfrac{15\times100}{16\times100}-\dfrac{16\times101}{17\times101}\right)\)
\(=\left(\dfrac{15}{16}+\dfrac{1}{17}\right)-\left(\dfrac{15}{16}-\dfrac{16}{17}\right)\)
\(=\dfrac{15}{16}+\dfrac{1}{17}-\dfrac{15}{16}+\dfrac{16}{17}=\dfrac{1}{17}+\dfrac{16}{17}=1\)
d) \(D=\left(\dfrac{1}{2^2}-1\right)\left(\dfrac{1}{3^2}-1\right)...\left(\dfrac{1}{100^2}-1\right)\)
\(=-\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)...\left(1-\dfrac{1}{100^2}\right)\)
\(=-\dfrac{2^2-1}{2^2}.\dfrac{3^2-1}{3^2}.....\dfrac{100^2-1}{100^2}\)
\(=-\dfrac{\left(2^2-1\right)\left(3^2-1\right)...\left(100^2-1\right)}{2^2.3^2.....100^2}\)
\(=\dfrac{1.3.2.4.....99.101}{2^2.3^2.....100^2}=\dfrac{1.101}{2.100}=\dfrac{101}{200}\)
C= ( 151515:10101/161616:10101 + 17^9 :17^9/17^10:17^90)-(1500:100/1600 :100 - 1616:101/1717:101)
C=( 15/16 + 1/17)-( 15/16- 16/17)
C= 15/16 + 1/17 - 15/16 + 16/17
C= (15/16-15/16) + ( 1/17+16/17)
C= 1 + 1
C= 2
