a) Tìm cặp số nguyên n sao cho n chia hết cho 2n - 4

b) Tính tổng S = 1 - 2 + 2² - 2³ + 2⁴ - 2⁵ + 2⁶ - 2⁷ + ... - 2²⁰¹³ + 2²⁰¹⁴

c) Chứng minh :

\(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{7}\) + ... + \(\dfrac{1}{2012}\) - \(\dfrac{1}{2013}\) + \(\dfrac{1}{2014}\) < \(\dfrac{2}{5}\)

Giúp mình nhé:

a) Chứng minh rằng:

1-\(\dfrac{1}{2}\)+\(\dfrac{1}{3}\)-\(\dfrac{1}{4}\)+...+\(\dfrac{1}{2013}\)-\(\dfrac{1}{2014}\)=\(\dfrac{1}{1008}\)+\(\dfrac{1}{1009}\)+...+\(\dfrac{1}{2014}\)

b)Cho \(\dfrac{2n^2+1}{3}\)là số nguyên; n\(\in\)N. Chứng minh rằng: \(\dfrac{n}{3}\)và \(\dfrac{2n+3}{6}\)là phân số tối giản.

5\(\dfrac{8}{17}\): x + (-\(\dfrac{1}{17}\)) : x + 3\(\dfrac{1}{17}\): 17\(\dfrac{1}{3}\)= \(\dfrac{4}{17}\)

\(\dfrac{1}{1.4}\)+ \(\dfrac{1}{4.7}\)+ \(\dfrac{1}{7.10}\)+ ... + \(\dfrac{1}{x.\left(x+3\right)}\)= \(\dfrac{6}{19}\)

So sánh hai biểu thức A và B, biết rằng:

A = \(\dfrac{2012}{2013}\)+ \(\dfrac{2013}{2014}\) và B =\(\dfrac{2012+2013}{2013+2014}\).

a) \(\dfrac{2}{1^2}.\dfrac{6}{2^2}.\dfrac{12}{3^2}.\dfrac{20}{4^2}.\dfrac{30}{5^2}.....\dfrac{110}{10^2}.x=-20\)

b) \(\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2013}\right).x+2013=\dfrac{2014}{1}+\dfrac{2015}{2}+...+\dfrac{4025}{2012}+\dfrac{4026}{2013}\)

c) \(\left(\dfrac{1}{1.2}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\right).x=\dfrac{2012}{51}+\dfrac{2012}{52}+...+\dfrac{2012}{99}+\dfrac{2012}{100}\)