Sum of potencies with higher potency as clue I am supposed to calculate the following as simple as possible. Calcute: $$1 + 101 + 101^2 + 101^3 + 101^4 + 101^5 + 101^6 + 101^7$$ Tip: $$ 101^8 = 10828567056280801$$ I...--prophetes.ai

Sum of potencies with higher potency as clue I am supposed to calculate the following as simple as possible. Calcute: $$1 + 101 + 101^2 + 101^3 + 101^4 + 101^5 + 101^6 + 101^7$$ Tip: $$ 101^8 = 10828567056280801$$ I have absolutely no idea how this tip is supposed to help me. Do I still have to calculate each potency? Can I somehow solve it with 101^7 * (1 + 101) = 10828567056280801? As I am not allowed to use a calculator a simple technique for formulas like the one above would be welcome.

**Hint:** $$1 + x + x^2 + \dots + x^n = \frac{x^{n+1} - 1}{x - 1}.$$