Question

Calculati sumele :
a) S= 1+2+3+4+5+6.....................+20
b)S= 1+2+3+4...................+49
c) S=1+2+3.....................+100
d)1+2+3+4+...................+200

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Answer 1

a)S=20x21:2= 10x21=210
b)S=49x50:2=49x25=1225
c)S=100x101:2=50x101=5050
d)S=200x201:2=100x201=20100

Answer 2

$\displaystyle 1+2+3+4+5+6+...+20= \frac{20(20+1)}{2} = \frac{20 \times 21}{2} = \frac{420}{2} =210 \\ \\ 1+2+3+4+...+49= \frac{49(49+1)}{2} = \frac{49 \times 50}{2} = \frac{2450}{2} =1225 \\ \\ 1+2+3+...+100= \frac{100(100+1)}{2}= \frac{100 \times 101}{2} = \frac{10100}{2} =5050 \\ \\ 1+2+3+4+...+200= \frac{200(200+1)}{2} = \frac{200 \times 201}{2} = \frac{40200}{2} =20100$