logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Sequence and Series
0 votes

Sum of series $1^2$-$2^2$+$3^2$-$4^2$+$5^2$+.....+$1001^2$ is

$(a)\;501501\qquad(b)\;1001001\qquad(c)\;1001\qquad(d)\;501500$

Can you answer this question?
 
 

1 Answer

0 votes
Answer : (a) 501501
Explanation : $S=1^2-2^2+3^2-4^2+\;.....\;+1001^2$
$S=(1-2)(1+2)\;+(3-4)(3+4)\;+........\;(1001)^2$
$S=\;-[1+2+3+-----\;1000]\;+(1001)^2$
$=\;-\frac{1}{2}*(1000)\;(1001)\;+(1001)^2$
$=501501.$
answered Jan 20, 2014 by yamini.v
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...