# Thread: (FP1) summation of finite series using standard results

1. ## (FP1) summation of finite series using standard results

Find the sum of all even numbers between 2 and 200 inclusive, excluding those which are multiples of 3.
Bamboozled by the toggling of digits here, I need help to of you as to which is the right answer.
This may be a typo by the book's typist, who knows.

2. Hello,

Sum of all even numbers between 2 and 200 :
$2+4+ \dots + 200=2(1+2+\dots+100)=2 \sum_{n=1}^{100} n$

Among these (integers from 1 to 100), remove the ones in the form $3k$

Sum of all multiples of 3 between 1 and 100 :
$3+6+\dots+99=3(1+2+\dots+33)=3 \sum_{n=1}^{33} n$

So $S=2 \left( \sum_{n=1}^{100} n-3 \sum_{n=1}^{33} n\right)$

$S=2 \left(\frac{100 \times 101}{2}-3 \cdot \frac{33 \times 34}{2} \right)$

$S=2 \left(50 \times 101-3 \times 33 \times 17 \right)$

$S=6734$

3. ## Solved

Originally Posted by Moo
Hello,

Sum of all even numbers between 2 and 200 :
$2+4+ \dots + 200=2(1+2+\dots+100)=2 \sum_{n=1}^{100} n$

Among these (integers from 1 to 100), remove the ones in the form $3k$

Sum of all multiples of 3 between 1 and 100 :
$3+6+\dots+99=3(1+2+\dots+33)=3 \sum_{n=1}^{33} n$

So $S=2 \left( \sum_{n=1}^{100} n-3 \sum_{n=1}^{33} n\right)$
I misunderstood the question, thanks for helping me out.
$S=2 \left(\frac{100 \times 101}{2}-3 \cdot \frac{33 \times 34}{2} \right)$

$S=2 \left(50 \times 101-3 \times 33 \times 17 \right)$

$S=6734$
I misunderstood the question, thanks for helping me out