SIGMA_(j=3 to 7)_[j/(j+2)].
The second pattern emphasizes a sign change. This is always achieved with (-1)^n, so that if n is odd, the sign is minus (why?) and if n is even, the sign is plus. The first term is 1, or a^0, so it is convenient to start the summation from zero:
SIGMA_(j=0 to n)_[(-1)^j*(a^j)].