Question

Ex 23 va rog mult de tot dau coroana!!!

Answer 1

Răspuns:

Explicație pas cu pas:

a) 1/(1*2) +1/(2*3) + ...+1/(24*25) =

1-1/2 +2/2-1/3 + 1/3-1/4 +...+1/24 -1/25 =

1 - 1/25 = 24/25

Sub radical:

2*24*25/2(24/25) = 24^2, √(24^2) = 24

b) 1/2*2/3*3/4...*81/82 = 1/82  restul se simplifica

1/(1*2) +1/(2*3) + ...+1/(81*82) =

1-1/2 +2/2-1/3 + 1/3-1/4 +...+1/81 -1/82 =

1-1/82 = 81/82

1/82*81/82 = 81/82^2,  √(81/82^2) = 9/82

c) (√2 -1)/√2 = 1-1/√2

(√3-√2)/(√2*√3) = 1/√2 -1/√3,  ...

S =  1-1/√2 + 1/√2 -1/√3 + 1/√3 -1/√4+...+1/√63 -1/√64 =

1 -1/√64 = 1 -1/8 = 7/8