Giải giúp mh với nha

Đáp án + Giải thích các bước giải:

a) $\frac{2}{1.2.3}$ + $\frac{2}{2.3.4}$ + $\frac{2}{3.4.5}$ + ... + $\frac{2}{98.99.100}$ 

= $\frac{1}{1.2}$ - $\frac{1}{2.3}$ + $\frac{1}{2.3}$ - $\frac{1}{3.4}$ + ... + $\frac{1}{98.99}$ - $\frac{1}{99.100}$ 

= $\frac{1}{1.2}$ - $\frac{1}{99.100}$

= $\frac{1}{2}$ - $\frac{1}{9900}$

= $\frac{4949}{9900}$ 

b) $\frac{4}{2.4.6}$ + $\frac{4}{4.6.8}$ + $\frac{4}{6.8.10}$ + ... + $\frac{4}{96.98.100}$

= $\frac{1}{2.4}$ - $\frac{1}{4.6}$ + $\frac{1}{4.6}$ - $\frac{1}{6.8}$ + $\frac{1}{6.8}$ - $\frac{1}{8.10}$ + ... + $\frac{1}{96.98}$ - $\frac{1}{98.100}$

= $\frac{1}{2.4}$ - $\frac{1}{98.100}$

= $\frac{1}{8}$ - $\frac{1}{9800}$

= $\frac{153}{1225}$ 

c) $\frac{6}{3.6.9}$ + $\frac{6}{6.9.12}$ + $\frac{6}{9.12.15}$ + ... + $\frac{6}{93.96.99}$

= $\frac{1}{3.6}$ - $\frac{1}{6.9}$ + $\frac{1}{6.9}$ - $\frac{1}{9.12}$ + $\frac{1}{9.12}$ - $\frac{1}{12.15}$ + ... + $\frac{1}{93.96}$ - $\frac{1}{96.99}$

= $\frac{1}{3.6}$ - $\frac{1}{96.99}$

= $\frac{1}{18}$ - $\frac{1}{9504}$

= $\frac{527}{9504}$ 

d) $\frac{3}{6.9.12}$ + $\frac{3}{9.12.15}$ + ... + $\frac{3}{93.96.99}$ + $\frac{3}{96.99.102}$

= $\frac{1}{2}$ x ($\frac{6}{6.9.12}$ + $\frac{6}{9.12.15}$ + ... + $\frac{6}{93.96.99}$ + $\frac{6}{96.99.102}$ )

= $\frac{1}{2}$ x ($\frac{1}{6.9}$ - $\frac{1}{9.12}$ + $\frac{1}{9.12}$ - $\frac{1}{12.15}$ + ... + $\frac{1}{93.96}$ - $\frac{1}{96.99}$ + $\frac{1}{96.99}$ - $\frac{1}{99.102}$ )

= $\frac{1}{2}$ x ($\frac{1}{6.9}$ - $\frac{1}{99.102}$)

= $\frac{1}{2}$ x ($\frac{1}{54}$ - $\frac{1}{10098}$ )

= $\frac{1}{2}$ x $\frac{31}{1683}$

= $\frac{31}{3366}$ 

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