A-level maths help!

Hello, I am so confused about this question on how the mark scheme got a value of K+1 for the value of n in S2. So if someone could please explain it would be much appreciated!

(edited 10 months ago)

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Reply 1

mqb2766

Between 1 and 2k+1 there are k+1 odd numbers. Just sub a value k=1 or 2 or ... to check.

To derive there are (2k+1)-1 / 2 = k intervals, so k+1 odd numbers.

(edited 10 months ago)

Reply 2

skyeforster15

Original post by mqb2766

Between 1 and 2k+1 there are k+1 odd numbers. Just sub a value k=1 or 2 or ... to check.

To derive there are (2k+1)-1 / 2 = k intervals, so k+1 odd numbers.

But why did you divide by 2.
--> Never mind its because there are half the number of odd numbers.

(edited 10 months ago)

Reply 3

mqb2766

Original post by skyeforster15

But why did you divide by 2.

The first comment was the most useful, jiust stick simple number(s) in to check
so
1 is 1 odd number and corresponds to k=0
1,3 is 2 odd numbers and corresponds to k=1
1,3,5 is 3 odd numbers and corresponds to k=2
... So k+1 odd numbers

But as you ask the intevals are the number of intervals between odd numbers so
2k+1 - 1
will be double the number of intervals between odd numbers, so divide by 2 and add 1. Its the old fence post/fence panel problem.