Question

Tính nhanh

a, 100-98+96-94+......+4-2+1

b,[1-1/2] . [1-1/3] . [1-1/4] . ...... . [1-1/2018]

c,[1+1/2] . [1+1/3] . [1+1/4]. ..... .[1+1/2017]

Answer 1

a,  a có 51 số ,chia thành 25 cặp mỗi cặp hai số hạng (trừ số 1) 

Ta có (100-98)+(96-94)+...+(4-2)+1

=2.25+1

=51

b,1/2.2/3.3.4....2016/2017.2017/2018

1/2018

c,3/2.4/3....2018/2017

2018/2=1009

Answer 2

\(100-98+96-94+...+4-2+1\)

\(=2+2+...+2+1\)( có 50 ố 2 )

\(=2.50+1\)

\(=\)\(101\)

\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2018}\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2017}{2018}\)

\(=\frac{1}{2018}\)

\(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{2017}\right)\)

\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{2018}{2017}\)

\(=\frac{2018}{2}\)

\(=1009\)

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