Question

Va rog sa ma ajutati la asta: x=1+3+5+...+225

Answer 1

x=1+3+5+...+225
x=( 1+2+3+4+5+...+224+225)- (2+4+6+....+224)
x= 225*226:2 - 2 (1+2+3+...+112)
x=225*113-2*112*113:2
x=225*113-112*113
x=113(225-112)
x=113*113
x=12769

Answer 2

$\displaystyle 1+3+5+...+225 \\ 225=1+(n-1) \cdot 2 \\ 225=1+2n-2 \\ 2n=225-1+2 \\ 2n=226 \\ n=226:2 \\ n=113 \\ S_{113}= \frac{2+112 \cdot 2}{2} \cdot 113 \\ \\ S_{113}= \frac{2+224}{2} \cdot 113 \\ \\ S_{113}= \frac{226}{2} \cdot 113 \\ \\ S_{113}= 113 \cdot 113 \\ S_{113}= 12769$