Question

va rog dau coroana
ex 37​

Answer 1

37)

N1 = 1987 + 2(1 + 2 + 3 + ... + 1986)

Confurm sumei lui Gauss, 1 + 2 + ... + n = n(n+1) / 2

deci:

N1 = 1987 + 2 * 1986 * 1987 / 2 = 1987 + 1986 * 1987

Scoatem in fata 1987

N1 = 1987(1986 + 1) = 1987 * 1987 = 1987 ^ 2 ==> N1 patrat perf

N2 = 64 + 2 * 64 + ... + 49 * 64

N2 = 64(1 + 2 + ... + 49) = 64 * 50 * 49 / 2 = 64 * 25 * 49 = (8 * 5 * 7) ^ 2 ==> N2 patrat perf