1/2 + 1/6 + 1/12 + ... + 1/9900 + 1/10100

= 1/1.2 + 1/2.3 + 1/3.4 +... +1/99.100 + 1/100.101

= 1/1 - 1/2 + 1/2 + 1/3 - 1/3 + 1/4 +... + 1/99 - 1 / 100 + 1/100 - 1/101

= 1/1 - 1/101

= 100 /101

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+.....+\frac{1}{9900}+\frac{1}{10100}\)

=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.......+\frac{1}{99.100}+\frac{1}{100.101}\)

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{99}-\frac{1}{100}+\frac{1}{100}-\frac{1}{101}\)

=\(1-\frac{1}{101}\)

=\(\frac{100}{101}\)

a, \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+....+\frac{1}{10100}\)

=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{100.101}\)

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{100}-\frac{1}{101}\)

=\(1-\frac{1}{101}\)

=\(\frac{100}{101}\)

b,\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{512}\)

=\(\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{8}\right)+...+\left(\frac{1}{256}-\frac{1}{512}\right)\)

=\(1-\frac{1}{512}\)

=\(\frac{511}{512}\)

\(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{9900}+\frac{1}{10100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}+\frac{1}{100}-\frac{1}{101}\)

\(=1-\frac{1}{101}=\frac{100}{101}\)

a) trieu dang làm rồi

b)   A= 1/2 + 1/4+ 1/8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
A = 1 - 1/2 + 1/2- 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + 1/16 - 1/32 + 1/32 - 1/64 + 1/64 - 1/128 + 1/128 - 1/256 - 1/256 - 1/512
A = 1 - 1/512
A = 511/512

1/2 + 1/6 + 1/12 + 1/20 + ... + 1/9900

= 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + ... + 1/99.100

= 1 - 1/2 + 1/2 - 1/2 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/99 - 1/100

= 1 - 1/100

= 99/100 

Mk nhanh nhất đó

Đúng 100%

Tk mk mk tk lại

Cảm ơn bạn nhiều

Thank you very much

( ^ _ ^ )

99/100

Buổi chiều hôm nay cô giáo mới dạy cho mình mà nên mình chắc chắn 100%

a) đề sai

1/2 + 1/6 + 1/12 + ... + 1/132

= 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/11.12

= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/11 - 1/12

= 1 - 1/12

= 11/12

1/90 + 1/110 + 1/132 + ... + 1/10100

= 1/9.10 + 1/10.11 + 1/11.12 + ... + 1/100.101

= ... [như trên]

= 1/9 - 1/100

= 49/450

balabal;a

bài toán này làm = cách đứt ruột đó




thầy mk vừa dạy mk xong

Ta có: \(\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9900}\)

\(=\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{99.100}\)

 \(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

   \(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)

\(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{9900}\)

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

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

= \(1-\frac{1}{100}\)

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

**** cho mình nha

\(x-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-...-\frac{1}{9900}=7,5\)

\(x-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9900}\right)=7,5\)

\(x-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)=7,5\)

\(x-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)=7,5\)

\(x-\left(1-\frac{1}{100}\right)=7,5\)

\(x-\frac{99}{100}=7,5\)

\(\Rightarrow x=7,5+\frac{99}{100}=\frac{750}{100}+\frac{99}{100}\)

\(\Rightarrow x=\frac{849}{100}=8,49\)

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