1-2+3-4+5-6+.......... +999-1000 = ?

JeyaMurugan   13 years AGO

Ans: (1-2)+(3-4)+(5-6)+(7-8)+.....+(999-1000)
=(-1)+(-1)+(-1)+(-1)+.....+(-1)(here n is 500)
=-500

Like? Yes (11) | No (2)  

senthilkumaran   13 years AGO

In 1 to 10 it contain(-1+-1+-1+-1+-1)=-5..

so for 1 to 1000 it contain -500.

so answer is -500

Like? Yes (5) | No (1)  

balaji   13 years AGO

1 = 1,
1 − 2 = −1,
1 − 2 + 3 = 2,
1 − 2 + 3 − 4 = −2,
1 − 2 + 3 − 4 + 5 = 3,
1 − 2 + 3 − 4 + 5 − 6 = −3,
.
.
.
1-2+3-4+5-6+.......... +999-1000 =-500

Like? Yes (3) | No   

Karthik Pandiyan   13 years AGO

(1+3+5+7...+999)-(2+4+6+8+...+1000)
By Arithmetic progression Sum of n terms =n/2(first term+last term)

Sum=(500/2)(1+999) - (500/2)(2+1000)
sum =250(1000)-250(1002);
= 250(1000-1002)
=250(-2)
=-500

Like? Yes (2) | No   

SUDESHNA SEN   13 years AGO

1-2+3-4+5-6+.......... +999-1000
= (1+3+5+....+999)- 2(1+2+3+....+500)
= 500^2- 2*[(500*501)/2]
=250000- 250500
=-500..... Option 4)

Like? Yes (2) | No   

Trishita Dasgupta   13 years AGO

1-2+3-4+5-6+.......... +999-1000
= (1+3+5+....+999)- 2(1+2+3+....+500)
= 500^2- 2*[(500*501)/2]
=250000- 250500
=-500..... Option 4)

Like? Yes (2) | No   

Parbati Sen   13 years AGO

1-2+3-4+5-6+.......... +999-1000
= (1+3+5+....+999)- 2(1+2+3+....+500)
= 500^2- 2*[(500*501)/2]
=250000- 250500
=-500..... Option 4)

Like? Yes (2) | No   

SARBANI DAS GHOSH   13 years AGO

1-2+3-4+5-6+.......... +999-1000
= (1+3+5+....+999)- 2(1+2+3+....+500)
= 500^2- 2*[(500*501)/2]
=250000- 250500
=-500..... Option 4)

Like? Yes (3) | No (1)  

Dr.Dipin Singh   13 years AGO

1-2+3-4+5-6+.......... +999-1000 = -500.
1-2=-1
3-4=-1
5-6=-1
..

so every group of two consecutive numbers in series gives -1.

so 500 groups will give result as -500.

Like? Yes (1) | No   

Dimple   13 years AGO

There are 500 pairs and each pair gives a value of -1.

like 1-2=-1;
3-4=-1;..
..
..so on
999-1000=-1

Like? Yes (1) | No   

sanjib biswas   13 years AGO

1-2+3-4+5-6+.......... +999-1000
= (1+3+5+....+999)- 2(1+2+3+....+500)
= 500^2- 2*[(500*501)/2]
=250000- 250500
=-500..... Option 4)

Like? Yes (2) | No (1)  

TAPAN SINGHA   13 years AGO

1-2+3-4+5-6+.......... +999-1000
= (1+3+5+....+999)- 2(1+2+3+....+500)
= 500^2- 2*[(500*501)/2]
=250000- 250500
=-500..... Option 4)

Like? Yes (1) | No   

Tridib Das   13 years AGO

1-2+3-4+5-6+.......... +999-1000
=(1+2+3+4+...........+999+1000) -4-8-12-16-20....-2000)
==(1+2+3+4+...........+999+1000) -4(1+2+3+4....+500)
=1000(1+1000)/2 -4{500(1+500)/2} [as sum of the consecutive numbers=n(a+l)/2]
=500500-501000
=-500

Like? Yes (1) | No   

Achelal Sharma   13 years AGO

solving this we get
1+3+5+7+9+....+999-(2+4+6+8+....+1000)
=> 500^2-(500)(501)
=>-500

Like? Yes (1) | No   

A J V   13 years AGO

1-2+3-4+5-6+...+999-1000 ---> -1-1-1-1...-1=-500.

Like? Yes (1) | No (1)  

YadeeshKumar   13 years AGO

1-2+3-4+5-6+.......... +999-1000
=(1+3+5+7+...999)-(2+4+6+...+1000)
=(1+3+5+7+...999)-2(1+2+3...+500)
formula
1+2+..n=(n*(n+1))/2
1+3+5+7..+(2n-1)=n^2
therefore
=500^2-(2(500*501)/2)
=500^2-500*501
=500(500-501)
=500(-1)
=-500

Like? Yes (1) | No (1)  

S. Singh   13 years AGO

1-2+3-4+5-6+.......... +999-1000 = -1-1 -1-1.... -1 = -1*500 ( for 500 groups ) = -500

Like? Yes (1) | No (1)  

Mamon Sengupta   13 years AGO

1-2+3-4+5-6+.......... +999-1000
= (1+3+5+....+999)- 2(1+2+3+....+500)
= 500^2- 2*[(500*501)/2]
=250000- 250500
=-500..... Option 4)

Like? Yes (1) | No (1)  

ASHOK ROY   13 years AGO

1-2+3-4+5-6+.......... +999-1000
= (1+3+5+....+999)- 2(1+2+3+....+500)
= 500^2- 2*[(500*501)/2]
=250000- 250500
=-500..... Option 4)

Like? Yes (1) | No (1)  

ANIRBAN CHATTERJEE   13 years AGO

1-2+3-4+5-6+.......... +999-1000
= (1+3+5+....+999)- 2(1+2+3+....+500)
= 500^2- 2*[(500*501)/2]
=250000- 250500
=-500..... Option 4)

Like? Yes (1) | No (1)  

aparna   13 years AGO

1-2+3-4+5-6+.......... +999-1000
= (1+3+5+....+999)- 2(1+2+3+....+500)
= 500^2- 2*[(500*501)/2]
=250000- 250500
=-500..... Option 4)

Like? Yes (1) | No (1)  

Bimal   13 years AGO

1-2+3-4+5-6+.......... +999-1000 = (1-2)+(3-4)+(5-6)+.......... +(999-1000) = -1-1-1-1.... 500 times = -500

Like? Yes (1) | No (1)  

samir    13 years AGO

1-2+3-4+5-6+.......... +999-1000
= (1+3+5+....+999)- 2(1+2+3+....+500)
= 500^2- 2*[(500*501)/2]
=250000- 250500
=-500..... Option 4)

Like? Yes (1) | No (1)  

PINKU SUD   13 years AGO

1-2+3-4+5-6+.......... +999-1000
= (1+3+5+....+999)- 2(1+2+3+....+500)
= 500^2- 2*[(500*501)/2]
=250000- 250500
=-500..... Option 4)

Like? Yes (1) | No (1)