Question

[Bích Ngọc]

Rút gọn:

a) 1/n - 1/n-1

b)1/2 + 1/2.3 + 1/3.4+ ... + 1/99.100

c) 1/15+ 1/35 + 1/63 + 1/99 + 1/143

d) 1/3 + 1/6 + 1/10 + 1/15 + 1/24 + 1/28

e) 1/2 + 1/2^2 + 1/2^3 + 1/2^100

 Các bạn giúp mình với.Thanks

Answer 1

[★๖ۣۜßảo๖ۣۜPɦα♏๖ۣۜ[EηgĻïšħ☯€lub]★]

\(a;\frac{1}{n}-\frac{1}{n-1}=\frac{n-1-n}{n\left(n-1\right)}=-\frac{1}{n\left(n-1\right)}\)

Answer 2

[Lê Tuấn Nghĩa]

a)  \(\frac{1}{n}-\frac{1}{n-1}=\frac{n-1-n}{n\left(n-1\right)}=-\frac{1}{n\left(n-1\right)}\)

b)  \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}=1-\frac{1}{100}=\frac{99}{100}\)(cái này là 1 tính chất nha bn ! tìm hiểu thêm nhé )

c)đặt   C= \(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}\)

        => 2C = \(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}=\frac{1}{3}-\frac{1}{13}=\frac{10}{39}\)

=>   C=5/39

d) Ý d) lm tương tự ý c nha 

e)  đặt E =\(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{100}}\)

   =>   2E=\(1+\frac{1}{2}+...+\frac{1}{2^{99}}\)

lấy 2E-E =\(1+\frac{1}{2}+...+\frac{1}{2^{99}}-\frac{1}{2}-\frac{1}{2^2}-...-\frac{1}{2^{100}}=1-\frac{1}{2^{100}}\)

=.> E=1 - \(\frac{1}{2^{100}}\)