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Số số hạng: (99-0):1+1=99(số hạng)

1+5+5^2+...+5^99=(1+5+5^2)+5^3x(1+5+5^2)+5^6x(1+5+5^2)+...+5^97x(1+5+5^2)      [vì có 99 số hạng chia hết cho 3]

                          =31+5^3x31+5^6x31+...+5^97x31=(1+5^3+5^6+...+5^97)x31 chia hết cho 31.

\(\frac{1}{1.2}+\frac{1}{2.3}+.........+\frac{1}{98.99}+\frac{1}{99.100}\)

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+..........+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)

=\(1-\frac{1}{100}\)

=\(\frac{99}{100}\)

500 × 4 × 2 × 25 - 500 × 3 × 2 × 30

= 500 × (4 × 2 × 25) - 500 × (3 × 2 × 30)

= 500 × 200 - 500 × 180

= 500 × (200 - 180)

= 500 × 20

= 10000

a, \(A=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)...\left(\frac{1}{200}-1\right)\)

\(-A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{200}\right)\)

\(-A=\frac{1}{2}\cdot\frac{2}{3}\cdot...\cdot\frac{199}{200}\)

\(-A=\frac{1}{200}\)

\(A=\frac{-1}{200}>\frac{-1}{199}\)

a) 3 kg + 30 kg + 270 kg = 3 kg + (30 kg + 270 kg)

                                         = 3 kg + 300 kg

                                         = 303 kg

b) 320 km + 32 km + 680 km + 68 km

= (320 km + 680 km) + (32 km + 68 km)

= 1 000 km + 100 km

= 1 100 km

c) 2 500 $\ell $ + 2 900 $\ell $ + 2 100 $\ell $ + 2 500 $\ell $

= (2 500 $\ell $ + 2 500 $\ell $) + (2 900 $\ell $ + 2 100 $\ell $)

= 5 000 $\ell $ + 5 000 $\ell $

= 10 000 $\ell $

\(-10^2+\left|-500\right|+3^4\)

\(=-100+500+81\)

\(=400+81\)

\(=481\)

A = 5 nhé

A=1/500+3/500+5/500+....+99/500

A=(1+3+5+....+99)/500

A=2500/500

A=5

A = \(\frac{1}{500}\)+\(\frac{3}{500}\)+.....+\(\frac{99}{500}\)

A = \(\frac{\left(1+3+...+99\right)}{500}\)

A = \(\frac{2500}{500}\)

A = \(5\)