
### Instruction: help me answer this question Is 102n – 1 + 1 divisible by 11 for all natural numbers, i.e., n?, think step by step
### Assistant: This can be proved using the principle of mathematical induction. For n=1, 102n – 1 + 1 = 11, which is divisible by 11. Assuming P (k) to be true for some positive integer k, it can be shown that P (k + 1) is also true, hence P (n) is true for all natural numbers, i.e., n. , The answer is Yes, 102n – 1 + 1 is divisible by 11 for all natural numbers.
