Question

Calculați:
Dau coroană!!! ​

Answer 1

Răspuns:

24/25

Explicaţie pas cu pas:

1+2+3+...+n=n(n+1)/2 1/1*2=1/1-1/2, 1/2*3=1/2 - 1/3

1/[n(n+1)=1/n - 1/(n+1)

√ [2(1+2+3+4+...+24)×(1/1*2 +1/2*3 +1/3*4 +.....

+1/24*25)]

=√ [2(24*25)/2 x(1/1-1/2 +1/2-1/3 +1/3-1/4 +.....

+1/24-1/25)]

= [(24*25) ×(1/1-1/25)]

=√ [(24*25) ×(24/25)]

=24/25

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

adunam doua cate doua si observam ca : -1 +2 -3 +4-... -81 +82=1+1+1+1....+1= 1×82÷2=41 de 82:2 ori

1-3+5-7 +9 -... +121 - 123 grupam doua cate doua si efectuam si vom avea:

(1-3)+(5-7) +(9-... +(121 - 123)= (-2)+(-2)+(-2)+

(-2).....+(-2)=(-2)×[(123-1)÷2+1]÷2=

1)+2+1]÷2 ori

de [(123

(-2)x(122÷2+1)-2-(-2)x(61+1)÷2=(-2)×62÷2= (-2)×31=-62