What is the easiest way to find the sum of all the numbers
$1, 2, 3, ..., 3¹⁰⁰⁰⁰⁰$ that are not divisible by 3,
possibly by using a handheld calculator and avoiding computer processing?
What is the easiest way to find the sum of all the numbers
$1, 2, 3, ..., 3¹⁰⁰⁰⁰⁰$ that are not divisible by 3,
possibly by using a handheld calculator and avoiding computer processing?
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Hints: 1) How many numbers in that range are multiples of 3? 2) If you divide each of those numbers by 3, you get 1, 2, ..., k. What is the sum of those numbers? 3) Now add the numbers from 1 to $3^{100000}$ and subtract the sum above.