def test_telescopic_sums():
#checks also input 2 of comment 1 issue 1028
assert Sum(1/k - 1/(k+1),(k,1,n)).doit() == 1 - 1/(1 + n)
f = Function("f")
assert Sum(f(k)-f(k+2),(k,m,n)).doit() == -f(1+n) - f(2+n) + f(m) + f(1+m)
assert Sum(cos(k)-cos(k+3),(k,1,n)).doit() == -cos(1 + n) - cos(2 + n) - \
cos(3 + n) + cos(1) + cos(2) + cos(3)
# dummy variable shouldn't matter
assert telescopic(1/m, -m/(1+m),(m, n-1, n)) == \
telescopic(1/k, -k/(1+k),(k, n-1, n))
assert Sum(1/x/(x - 1), (x, a, b)).doit() == -((a - b - 1)/(b*(a - 1)))
def test_telescopic_sums():
#checks also input 2 of comment 1 issue 4127
assert Sum(1/k - 1/(k + 1), (k, 1, n)).doit() == 1 - 1/(1 + n)
f = Function("f")
assert Sum(
f(k) - f(k + 2), (k, m, n)).doit() == -f(1 + n) - f(2 + n) + f(m) + f(1 + m)
assert Sum(cos(k) - cos(k + 3), (k, 1, n)).doit() == -cos(1 + n) - \
cos(2 + n) - cos(3 + n) + cos(1) + cos(2) + cos(3)
# dummy variable shouldn't matter
assert telescopic(1/m, -m/(1 + m), (m, n - 1, n)) == \
telescopic(1/k, -k/(1 + k), (k, n - 1, n))
assert Sum(1/x/(x - 1), (x, a, b)).doit() == -((a - b - 1)/(b*(a - 1)))
