Question

S=1+3+5+...+199
Sa se afle suma numerelor naturale! Mie imi da cu rest.E bine?

Answer 1

ai gauss pentru numere impare, care spune asa
1+3+5+...+2n-1=n*n

tu ai
1+3+5+...+199

Deci 2n-1=199
2n=199+1
2n=200
n=100

Suma va fi egal cu 100*100=10000

Answer 2

$\displaystyle 1+3+5+...+199= \\ \\ =1+2+3+4+5+...+199-(2+4+6+...+198)= \\ \\ = \frac{199(199+1)}{2} -2(1+2+3+...+99)= \\ \\ =\frac{199 \times 200}{2} -2 \times \frac{99(99+1)}{2} = \frac{39800}{2} -2 \times \frac{99 \times 100}{2} = \\ \\ =19900-\not2 \times \frac{9900}{\not2} =19900-9900=10000$