Răspuns:
7/8
Explicație pas cu pas:
a = (√2-1)/√2 + (√3-√2)/√6 + (√4-√3)/√12 +......+(√64-√63)/√4032 = ?
--------
(√2-1)/√2 = √2/√2 - 1/√2 = 1 - 1/√2
(√3-√2)/√6 = √3/√6 - √2/√6 = 1/√2 - 1/√3
(√4-√3)/√12 = √4/√12 - √3/√12 = 1/√3 - 1/√4
(√5-√4)/√20 = √5/√20 - √4/√20 = 1/√4 - 1/√5
.....................
(√64-√63)/√4032 = √64/√4032 - √63/√4032 = 1/√63 - 1/√64
-------------------
=>
a = 1 - 1/√2+1/√2 - 1/√3+1/√3 - 1/√4+1/√4 - 1/√5+.....+1/√63 - 1/√64=>
a = 1 - 1/√64 = ⁸⁾1 - 1/8 = (8-1)/8 = 7/8
a = 7/8
Show life that you have a thousand reasons to smile
© Copyright 2024 DOKU.TIPS - All rights reserved.
Răspuns:
7/8
Explicație pas cu pas:
a = (√2-1)/√2 + (√3-√2)/√6 + (√4-√3)/√12 +......+(√64-√63)/√4032 = ?
--------
(√2-1)/√2 = √2/√2 - 1/√2 = 1 - 1/√2
(√3-√2)/√6 = √3/√6 - √2/√6 = 1/√2 - 1/√3
(√4-√3)/√12 = √4/√12 - √3/√12 = 1/√3 - 1/√4
(√5-√4)/√20 = √5/√20 - √4/√20 = 1/√4 - 1/√5
.....................
(√64-√63)/√4032 = √64/√4032 - √63/√4032 = 1/√63 - 1/√64
-------------------
=>
a = 1 - 1/√2+1/√2 - 1/√3+1/√3 - 1/√4+1/√4 - 1/√5+.....+1/√63 - 1/√64=>
a = 1 - 1/√64 = ⁸⁾1 - 1/8 = (8-1)/8 = 7/8
a = 7/8