Home
Class 10
MATHS
Using the principle of Mathematical Indu...

Using the principle of Mathematical Induction , `forall n in N`, prove that `1^2+2^2+3^2+.....n^2=(n(n+1)(2n+1))/6`

A

`(n^2(n-1)^2)/2`

B

`(n(2n+1))/4`

C

`(n(n+1)(2n+1))/6`

D

`((n+1)^2)/2`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • PROGRESSIONS

    VGS PUBLICATION-BRILLIANT|Exercise Creative Bits for CCE Model Examination|129 Videos
  • PROBABILITY (MULTIPLE CHOICE QUESTION)

    VGS PUBLICATION-BRILLIANT|Exercise PROBABILITY (MULTIPLE CHOICE QUESTION)|20 Videos
  • PROGRESSIONS (MULTIPLE CHOICE QUESTION)

    VGS PUBLICATION-BRILLIANT|Exercise PROGRESSIONS (MULTIPLE CHOICE QUESTION)|20 Videos

Similar Questions

Explore conceptually related problems

Using the principle of finite Mathematical Induction prove that 1^2+(1^2+2^2)+(1^2+2^2+3^2)+.......n terms =(n(n+1)^2(n+2))/12,foralln in N

Using the principle of finite Mathematical Induction prove that 1.2.3+2.3.4+3.4.5.+………… upto n terms = n(n+1)(n+2)(n+3))/4,for all n in N

Using the principle of finite Mathematical Induction prove that 1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)+3^(2)) + "n terms" = (n(n+1)^(2)(n+2))/(12), AA n in N .

Using the principle of finite Mathematical Indcution prove that 2.3 + 3.4 + 4.5 + ……."upto n terms" = (n(n^(2)+6n+11))/(3) .

Using the principle of Mathematical Induction, Show that 49^n+16n-1 is divisible by 64, forall n in N .

Using the principle of Mathematical Induction, show that 2.4^(2n+1)+3^(3n+1) is divisible by 11, forall n in N

Using the principle of finite Mathematical Induction prove the following: (v) 3.5^(2n+1)+2^(3n+1) is divisible by 17, AA n in N .

Using the principle of finite Mathematical Induction prove the following: (iv) a+ar+ar^(2)+……..+"n terms" = (a(r^(n)-1))/(r-1) , r != 1 .

Using the principle of finite Mathematical Induction prove the following: (vi) 2+3.2+4.2^(2)+………."upto n terms" = n.2^(n) .

Use mathematical induction to prove that statement 1^(3) + 2^(3) + 3^(3) + . . . + n^(3) = (n^(2) (n + 1)^(2))/( 4) , AA n in N