Question

Caut rezolvarea sau macar o formula la un exercitiu de genul :
x= 1+3+5+...+101
Dau coroana

Answer 1

$\displaystyle 1+3+5+...+101 \\ 101=1+(n-1) \cdot 2 \\ 101=1+2n-2 \\ 2n=101-1+2 \\ 2n=102 \\ n=102:2 \\ n=51 \\ S_{51}= \frac{2+50 \cdot 2}{2} \cdot 51 \\ S_{51}= \frac{2+100}{2} \cdot 51 \\ S_{51}= \frac{102}{2} \cdot 51 \\ S_{51}=51 \cdot 51 \\ S_{51}=2601 \\ \boxed{x=2601}$