Tính a) (0,375 - 0,3 + 3/11 + 3/12)/ (0,625 - 0,5 + 5/11 + 5/12) b) Tính nhanh: C= C= 1/100 - 1/(100.99) - 1/(99.98) - ... - 1/3.2 - 1/2.1 c) M = 2^2010 - ( 2^2009 + 2^2008 + ...+ 2^1 + 2^0 ) Trả lời nhanh giúp em vs ạ

Giải thích các bước giải:

Bài 1:

b.Ta có:

$\dfrac{1}{n(n-1)}=\dfrac{n-(n-1)}{n(n-1)}=\dfrac{n}{n(n-1)}-\dfrac{n-1}{n(n-1)}=\dfrac{1}{n-1}-\dfrac{1}{n}$

$\rightarrow C=\dfrac{1}{100}-(\dfrac{1}{100.99}+\dfrac{1}{99.98}+..+\dfrac{1}{2.1})$

$\rightarrow C=\dfrac{1}{100}-(-\dfrac{1}{100}+\dfrac{1}{99}-\dfrac{1}{99}+\dfrac{1}{98}-..-\dfrac{1}{2}+1)$

$\rightarrow C=\dfrac{1}{100}-(-\dfrac{1}{100}+1)$

$\rightarrow C=\dfrac{1}{100}+\dfrac{1}{100}-1$

$\rightarrow C=\dfrac{1}{50}-1$

c.Ta có:

$A=2^{2009}+2^{2008}+..+2^1+2^0$

$\rightarrow 2A=2^{2010}+2^{2009}+..+2^2+2^1$

$\rightarrow 2A-A=2^{2010}-2^0$

$\rightarrow A=2^{2010}-1$

$\rightarrow M=2^{2010}-A=2^{2010}-(2^{2010}-1)$

$\rightarrow M=1$