When the Sum Stays Below One

★ 7/10sequences Telescoping inequality Casework

Problem

A sequence $\{a_n\}$ has general term

a_n = \frac{nx}{(x+1)(2x+1)\cdots(nx+1)}, \quad n \in \mathbb{N}^*.

Find all real numbers $x$ for which

a_1 + a_2 + \cdots + a_{2018} < 1.

Answer

Solution

Difficulty	7/10
Topics	sequences, Telescoping, inequality, Casework

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.