Home
Class 12
MATHS
Find the sum 11^2-1^2+12^2-2^2+13^2-3^2+...

Find the sum `11^2-1^2+12^2-2^2+13^2-3^2+……+20^2-10^2`

Text Solution

Verified by Experts

The correct Answer is:
1400
`11^(2)-1^(2)+12^(2)-2^(2)+13^(2)-3^(2)+…+20^(2)-10^(2)`
`=(1^(2)+2^(2)+3^(2)+….+20^(2))-2(1^(2)+2^(2)+3^(2)+…+10^(2))`
`=(20xx21xx41)/6-2xx(10xx11xx21)/6`
`=(20xx21)/6(41-21)`
=1400
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.9|9 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise EXERCIESE ( SINGLE CORRECT ANSWER TYPE )|93 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.7|4 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

Find the value of 11^2+12^2+13^2++20^2dot

Find the sum 1^2+(1^2+2^2)+(1^2+2^2+3^2)+ up to 22nd term.

Find the sum of the series 1^2-2^2+3^2-4^2+\ldots-{2008}^2+{2009}^2

Find the sum (1^2)/2-(3^2)/(2^2)+(5^2)/(2^3)-(7^2)/(2^4)+....oodot

Find the sum to n terms of each of the series in 1^2 + (1^2 + 2^2) + (1^2 + 2^2 + 3^2) + ...

Find the sum : 3.1^2+4.2^2+5.3^2+.... upto n terms.

Find the 10th term of (2x^2+1/x)^12 .

Find the sum to n terms : 1/2+3/2^2+5/2^3+...+(2n-1)/2^n

Find the sum of the series : 1^(2) + 2^(2)x + 3^(2)x^(2) + 4^(2) x^(3)+…. oo