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Sn=1+3+5+7+...+(2n+1)

-Să se calculeze suma.

Help plz, ms


Răspuns :

S = 1 + 3 + .. + 2n + 1


S = (1 + 2 + 3 + .. 2n + 1) - (2 + 4 + .. + 2n + 2)


S = (2n + 1)·2n/2 - 2·[1 + 2 + (n + 1)]


S = (2n + 1)·2n/2 - 2·[(n + 1)·n/2]


S = (2n + 1)·n - (n + 1)·n


S = 2n² + n - n² - n


S = n²