Home
Class 11
MATHS
If sum(k=1)^(n)k=210, find the value of ...

If `sum_(k=1)^(n)k=210,` find the value of `sum_(k=1)^(n)k^(2).`

Text Solution

Verified by Experts

The correct Answer is:
2870
`(1+2+3+...+n)=210rArr (1)/(2)n(n+1)=210rArr n^(2)+n-420=0`
`rArr (n+21)(n-20)=0 rArr n=20.`
`therefore (1^(2)+2^(2)+3^(2)+...+n^(2))=(1)/(6)n(n+1)(2n+1), " where " n =20`
`=((1)/(6)xx20xx21xx41)=2870.`
Promotional Banner

Topper's Solved these Questions

  • SOME SPECIAL SERIES

    RS AGGARWAL|Exercise EXERCISE 13A|25 Videos

  • SOLUTION OF TRIANGLES

    RS AGGARWAL|Exercise EXERCISE 18 B|3 Videos

  • STATISTICS

    RS AGGARWAL|Exercise EXERCISE 30D|5 Videos

Similar Questions

Explore conceptually related problems

If sum_(k=1)^(n)k=45, find the value of sum_(k=1)^(n)k^(3).

sum_(k=1)^n k^3=

If n is a positive integer SC_(k)=^(n)C_(k), find the value of (sum_(k=1)^(n)(k^(3))/(n(n+1)^(2)*(n+2))((C_(k))/(C_(k)-1))^(2))^(-1)

If n is a positive integer and C_(k)=.^(n)C_(k) then find the value of sum_(k=1)^(n)k^(3)*((C_(k))/(C_(k-1)))^(2)

If n is a positive integer and C_(k)=""^(n)C_(k) , then the value of sum_(k=1)^(n)k^(3)((C_(k))/(C_(k-1)))^(2) is :

If for n in N,sum_(k=0)^(2n)(-1)^(k)(2nC_(k))^(2)=A, then find the value of sum_(k=0)^(2n)(-1)^(k)(k-2n)(2nC_(k))^(2)

Evaluate : sum_(k=1)^n (2^k+3^(k-1))

Find the sum sum_(k=0)^n ("^nC_k)/(k+1)

Find the sum sum_(k=0)^n("^nC_k)/((k+1)(k+2))

Find the value of lim_(n rarr oo)sum_(k=1)^(n)((k)/(n^(2)+k))