Question

Combinări de16 luate câte 0+Combinări de 16 luate câte 2 +......+Combinări de 16luate câte 16​

Answer 1

combinari de 16 luate cate 0= combinari de 16 luate cate 16=1

combinari de 16 uate cate 1=combinari de 16 luate cate 15=16

combinari de 16 luate cate 2=combinari de 16 luate cate 14

si asa mai departe pana la combnari de 16 luate cate 7=combinari de 16 luate cate 9

iar combinari de 16 luate cate 8ramane asa

Acum reiau suma si va veni:

2 x combinari de 16 luate cate 0+ 2 x combinari de 16 luate cate 1+...... +2 x  combinari de 16 luate cate 7+ combinari de 16 luate cate 8=

2 x 1 + 2 x 16!/15! + 2 x 16!/14!2! + ...+ 2 x 16!/9!7! + 16!/8!8!=

2+2x16 + 2 x (15x16)/2 + ....+ 2x (10x11x12x13x14x15x16)/(2x3x4x5x6x7) + (9x10x11x12x13x14x15x16)/(2x3x4x5x6x7x8)=

2+32+240+1120+...+2x 11440+ 12870

incearca sa faci tu calculele si multe simplificari