Suppose 1/2 + 1/3 + 1/4 + ... + 1/x > 2.
What is the smallest possible value for x?
+487 Just listing out the terms, we get:
1/2+1/3=5/6
1/2+1/3+1/4=13/12
1/2+1/3+1/4+1/5=77/60
1/2+1/3+1/4+1/5+1/6=87/60
1/2+1/3+1/4+1/5+1/6+1/7=223/140
1/2+1/3+1/4+1/5+1/6+1/7+1/8=481/280
1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9=4609/2520
1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10=4861/2520
1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11=55991/27720(first number greater than 2)
From this, we can see the smallest integer value of x is 11. However, this way of listing out terms is slow, and if anybody else has an algebraic way, it would be much appreciated.
