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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Sequences and Series

NDA 2012 · Mathematics · Sequences and Series

Consider the following statements : 1. The sum of cubes of first 20...

Consider the following statements : 1. The sum of cubes of first 20 natural numbers is 44400. 2. The sum of squares of first 20 natural numbers is 2870. Which of the above statements is/are correct?

Options

  1. A11 only
  2. B22 only
  3. CBoth 11 and 22
  4. DNeither 11 nor 22

Correct answer

B. 22 only

Step-by-step solution

∵13+23+33+……+n3=(n(n+1)2)2∴13+23+33+…….+203=(20.212)2=(10×21)2=4410012+22+33+……+n2=16n(n+1)(2n+1)∴12+22+……+202=1620.21.41=2870\because \quad 1^3+2^3+3^3+\ldots \ldots+n^3=\left(\frac{n(n+1)}{2}\right)^2\therefore 1^3+2^3+3^3+\ldots \ldots.+20^3=\left(\frac{20.21}{2}\right)^2=(10 \times 21)^2=441001^2+2^2+3^3+\ldots \ldots+n^2=\frac{1}{6} n(n+1)(2 n+1)\therefore \quad 1^2+2^2+\ldots \ldots+20^2=\frac{1}{6} 20.21.41=2870
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