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.
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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.
a,Vế trái:
\(1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2013}-\dfrac{1}{2014}\)
\(=1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2014}-2\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{6}+...+\dfrac{1}{2014}\right)\)
\(=1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2014}-\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{1007}\right)\)
\(=\dfrac{1}{1008}+\dfrac{1}{2009}+...+\dfrac{1}{2014}\)
b,chưa có câu trả lời, sorry nha
Thanks.