ABSTRACT
Arithmetic-geometric progression:
(a+ bk)qk = a(1− qn)− b(n− 1)qn
1− q + bq(1− qn−1) (1− q)2 .
k = n(n+ 1)
2 .
2. n∑
k2 = 1
6 n(n+ 1)(2n + 1).
3. n∑
k3 = 1
4 n2(n+ 1)2.
4. n∑
k4 = 1
30 n(n+ 1)(2n + 1)(3n2 + 3n− 1).
Arithmetic-geometric progression:
(a+ bk)qk = a(1− qn)− b(n− 1)qn
1− q + bq(1− qn−1) (1− q)2 .
k = n(n+ 1)
2 .
2. n∑
k2 = 1
6 n(n+ 1)(2n + 1).
3. n∑
k3 = 1
4 n2(n+ 1)2.
4. n∑
k4 = 1
30 n(n+ 1)(2n + 1)(3n2 + 3n− 1).