# C1 Value Of NWatch

#1
HI SAY IF YOU WANT TO FIND THE SUM OF THE NATURAL NUMBERS upto 100
from 1

is n = 100 or 101,

also for example say some of all the even numbers etc upto 100, is it 50?

and sorry one more, say they give you last term as 20 and first term as 10, are the n values 10 or is 11?!

AHHHHHH
0
12 years ago
#2

Sn = n (a+l)/2

Sn = 100 (1+100) / 2

Sn = 5050
0
12 years ago
#3
HI SAY IF YOU WANT TO FIND THE SUM OF THE NATURAL NUMBERS upto 100
from 1

is n = 100 or 101,

also for example say some of all the even numbers etc upto 100, is it 50?

and sorry one more, say they give you last term as 20 and first term as 10, are the n values 10 or is 11?!

AHHHHHH

Count it on your Fingers or Toes.......???

10 11 12 13 14 15 16 17 18 19 20.......11 terms of course

from ath to bth term is always b-a+1 terms
0
12 years ago
#4
If you write all the numbers out...say 1 to n, you get

1,2,3......,n

and then in reverse order

n,n-1,......3,2,1

Then add both these up you get (n+1)+(n+1)..... n times
So n*(n+1) gives twice the sum of the numbers from 1 to 100.
So to get the sum you divide my two...i.e. n(n+1)/2 as mentioned.

If you want to find the sum of the numbers from 50 to 100 say. Then you can calculate the sum of the numbers from 1 to 100 and then subtract the sum of the numbers from 1 to 49.

For the even numbers, you could write them out as before
2,4,6.....2(n-1),2n
2n,2(n-1),....6,4,2

But then you can see that we have exactly the same numbers before but just times two...i.e. the total sum here will be twice that of the sum of the numbers from 1 to n
i.e. n(n+1). However, dont forget that n is the number of numbers you are adding up, so for n=10, in the first example you had 1+2+3...+9+10 but in the second it is 2+4+6....+20. So if you want the sum of the even numbers from 1 to 20, you have to divide n by 2 to get the value for n..i.e. the highest number in your sum is actually 2n. So the formula is actually n/2(n/2+1)=n^2/4+n/2 where n is the biggest (and presumably even) number in the sequence.

E.g. Say n(biggest number)=6, then sum=6^2/4+6/2=9+3=12=2+4+6 as needed.
0
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