2022 China's Math GaoKao (College Entrance Exams): Problem 17 (sequence and series)

From 2022 China's Math GaoKao (College Entrance Exams): Problem 17 (sequence, series).

[JosephineLiang-vk]

For the first part, I got the sequence 1, 3, 6, 10, 15... Which is just n(n+1)/2. But I do wonder if that is rigorous enough to get full marks 🤔

[magnetoninja]

Very easy like 3 minute solve, first you induct to find a_n is nth triangle number and then telescope series the summation by summing 2(1\n-1\(n+1))

[albe]

I see that you used the telescoping series to prove the second part, but couldn't you also use proof by induction to prove the second part as well?

[kundansingh]

I think this are only easy question of that exam

[chAD]

Try JEE Advanced exam of India 😢....this is nothing

[priyamchoubey]

What the hell china is doing man these are nothing near compared to the gid jee advanced