What is the answer to this math problem?

Question

1+2+3+4+5+6...(and so on)...997+998+999+1000?
Anyone who gets this right first will get the 10 points.
Hint: There is a formula for this type of question that will cut time dramatically.
Dont't BS about homework. This is not homework. Its july for Christ sake.

Answer 1

It is (1+1000)*1000/2 =500500

Answer 2

Let S = 1 + 2 + 3 + 4 + ... + 999 + 1000
Writing S in reverse:
S = 1000 + 999 + 998 + 997 + ... + 2 + 1

Adding the two expressions for S term by term, we get:
2S = 1001 + 1001 + 1001 + 1001 + ... + 1001 + 1001, where there are 1000 1001's being added.

Hence: 2S = 1000 x 1001
Consequently, S = 500 x 1001 = 500,500.

Alternatively, one could use the formula:

1 + 2 + 3 + 4 + ... + (N - 1) + N = N(N + 1)/2.

Answer 3

1 + 2 + ... + 500
+ 1000 + 999 + ... + 501

= 1001 + 1001 + ... + 1001

= 500 * 1001

= 500500

Answer 4

The formula to find out the sum of first n natural numbers is {n(n+1)} / 2

For example sum of first 10 natural numbers is 10(11)/2 = 55
In the similar way you can find it for 100 it is as follows
100(101)/2 = 5050.

Now finding for 1000 numbers. It is 1000(1001)/2 = 500500

Similarly you can do it for any numbers (first n Natural Numbers).

Hope you understood it.

Answer 5

if u add any numbers from 1 to 10 or 100 0r 1000 or 10000
the answer is easily get by dividing the last number by 2..
in ur question 1000/2=500

just append another 500 to that 500

so , ans.. is 500500

Answer 6

Let's give an answer without just formulas.

Think of the problem as building a triangle:

#
##
###
####
#####
...
and so on, up to 1000 rows. Question: how many squares do you need for this triangle? It becomes a lot easier if we make a copy of the triangle, turn it around and combine it with the original triangle:

# ######################...
## #####################...
### ####################...
#### ###################...
##### ##################...
.....
The result is a rectangle of 1000 rows and 1001 columns. The number of squares in this rectangle is

1000 x 1001 = 1001000

Because the rectangle consists of two triangles, each triangle has half this number of squares,

1001000 / 2 = 500500.

Answer 7

(n+1)*n/2 ;
thus for n=1000 you get 1001*500 = 500500

Answer 8

The formula is 1+2+3+.................................+n = n(n+1) / 2

using the formula
1+2+3+.................................+1000 = 1000(1000+1) / 2
= 1000*1001 / 2
= 1001000 / 2
= 500500

Answer 9

lol, im gonna have to agree with the others and say its 500500..... i am too damn lazy to acctually work that out tho, :)


plus, the others have all these equations and stuff.... they really seem like they know what they're doing, lol

Answer 10

41748