Question

S=1+3+5+....+101 sume gauss

Answer 1

nr term(101-1):2+1=
100:2+1
50+1
51
suma(101+1)*51:2
102*5:2
5 202:2
2 601

Answer 2

$\displaystyle S=1+3+5+...+101 \\ \\ 101=1+(n-1) \times 2 \\ \\ 101=1+2n-2 \\ \\ 2n=101-1+2 \\ \\ 2n=102 \\ \\ n= \frac{102}{2} \\ \\ n=51$

$\displaystyle S_5_1= \frac{2+50 \times 2}{2} \times 51 \\ \\ S_5_1= \frac{2+100}{2} \times 51 \\ \\ S_5_1= \frac{102}{2} \times 51 \\ \\ S_5_1=51 \time 51 \times 51 \\ \\ S_5_1=2601$