Question

doar ex 4 din poza
multumesc​

Answer 1

Răspuns:

Explicație pas cu pas:

x = 32768

Answer 2

Răspuns:

C₁₆⁰ + C₁₆² + C₁₆⁴+ ...+ C₁₆¹⁶=S

C₁₆⁰=C₁₆¹⁶=1

C₁₆²= 16!/ 14!*2!

C₁₆¹⁴= 16!/ 2!*14! ===> C₁₆²=C₁₆¹⁴

C₁₆⁴= 16!/ 12!* 4!

C₁₆¹²= 16!/ 4!* 12! ==> C₁₆⁴=C₁₆¹²

C₁₆⁶= 16!/ 10!*6!

C₁₆¹⁰=16!/6!*10! ===> C₁₆⁶=C₁₆¹⁰

C₁₆⁸=C₁₆⁸= term.de mijloc

Suma S= 2*1 + 2*C₁₆²+ 2*C₁₆⁴+ 2*C₁₆⁶ + C₁₆⁸

S=2 *( 1+ 16*15*14! / 14!*2 + 16*15*14*13*12!/ 12!*24 + 16*15*14*13*12*11*10!/10!* 720) + 16!/ 8!*8!

S= 2*( 1+8*15+ 10*13*14+4*11*13*14) + 16*15*14*...*9/8*7*6*5*..*1!

S= 2*( 1+ 120+ 13*14*(10+44) ) + 9*10*11*13

S= 2*( 121+ 13*14*54) + 9*10*11*13

S= 242 + 2*13*14*9*6 + 9*10*11*13

S= 242+ 13*9*2(14*6+ 5*11)

S=242+ 234*(84+55)

S= 242+234*139

S= 242+32 526 = 32 768