Question

dau coroana

pls scrie pe o foaie rezolvarea​

Answer 1

Explicație pas cu pas:

$a = \dfrac{ \sqrt{1} - \sqrt{2} }{ \sqrt{1 \cdot 2} } + \dfrac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2 \cdot 3} } + \dfrac{ \sqrt{3} - \sqrt{4} }{ \sqrt{3 \cdot 4} } + ... + \dfrac{ \sqrt{287} - \sqrt{288} }{ \sqrt{287 \cdot 288} }+ \dfrac{ \sqrt{288} - \sqrt{289} }{ \sqrt{288 \cdot 289} } =$

$= \dfrac{ \sqrt{1}}{ \sqrt{1} \cdot \sqrt{2}} - \dfrac{ \sqrt{2}}{ \sqrt{1} \cdot \sqrt{2}} + \dfrac{ \sqrt{2}}{ \sqrt{2} \cdot \sqrt{3}} - \dfrac{ \sqrt{3}}{ \sqrt{2} \cdot \sqrt{3}} + \dfrac{ \sqrt{3}}{ \sqrt{3} \cdot \sqrt{4}} - \dfrac{ \sqrt{4}}{ \sqrt{3} \cdot \sqrt{4}} + ... + \dfrac{ \sqrt{287}}{ \sqrt{287} \cdot \sqrt{288}} - \dfrac{ \sqrt{288}}{ \sqrt{287} \cdot \sqrt{288}} + \dfrac{ \sqrt{288}}{ \sqrt{288} \cdot \sqrt{289}} - \dfrac{ \sqrt{289}}{ \sqrt{288} \cdot \sqrt{289}}$

$= \dfrac{1}{\sqrt{2}} - \dfrac{1}{ \sqrt{1}} + \dfrac{1}{\sqrt{3}} - \dfrac{1}{ \sqrt{2}} + \dfrac{1}{\sqrt{4}} - \dfrac{1}{ \sqrt{3}} + ... + \dfrac{1}{\sqrt{288}} - \dfrac{1}{ \sqrt{287}} + \dfrac{1}{\sqrt{289}} - \dfrac{1}{ \sqrt{288}}$

$= - 1 + \dfrac{1}{ \sqrt{289} } = \dfrac{1}{ \sqrt{ {17}^{2} } } - 1 = \dfrac{1}{17} - 1$

$= \dfrac{1 - 17}{17} = \bf - \dfrac{16}{17} \in \mathbb{Q}$

q.e.d.

Answer 2

Răspuns:

Explicație pas cu pas: