Q6) use any method to prove or disprove the following: 1+ n +

Q6) Use any method to prove or disprove the following:
1+ n + n^2 + .. + n^m = O(n^m).

Q7) Use any method to simplify each of the following by replacing the
sum with a closed formula or a function in n.

– O(1 + 2 + 3 +… + n).
– O(2 + 4 + 6 +… + 2n).
– O(1+ a + a^2 +… + a^(n-1)), where a is a constant not equal to 1.
– O(a+ a^2 + a^3 + .. + a^n), where a is a constant not equal to 1.