Question

1-2+3-4+5-6+...+101-102​

Answer 1

PRIMA MODALITATE

Grupam cate doua numere astfel:

1-2;3-4;5-6;7-8;...;101-102

Rezulta ca toate grupele de numere dau -1, asadar 1-2+3-4+5-6+...+101-102=cardA×-1

unde A={1;2;3;...;51}

cardA=51-1+1=51=>1-2+3-4+5-6+...+101-102=-51

A DOUA MODALITATE

1-2+3-4+5-6+...+101-102=

1+3+5+...+101-2(1+2+3+...+51)

101=2n-1, pentru care 1+3+5+...+101=n^2

n=51=>1+3+5+...+101=51^2

2(1+2+3+4+...+51)=2÷2×51×52=51×52

1-2+3-4+5-6+...+101-102=51×51-51×52=

51(51-52)=51×-1=-51

Answer 2

Răspuns:

Explicație pas cu pas:

1-2+3-4+5-6+...+99-100+101

-102  = (1+3+5+...+101) - (2+4+6+...+100-102)

(101-1):2+1=51