Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
141 views
in Mathematics by (114k points)
closed by

Consider the following statements:

1. The sum of cubes of first 20 natural numbers is 444000.

2. The sum of squares of first 20 natural numbers is 2870.

Which of the above statements is / are correct?


1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
5. None of these

1 Answer

0 votes
by (115k points)
selected by
 
Best answer
Correct Answer - Option 2 : 2 only

Concept:

Sum of cubes of natural numbers:

The sum of the cubes of first n natural numbers is given by:

\(\rm \displaystyle\sum_{k=1}^{n}k^3 = \left[\dfrac{n(n+1)}{2}\right]^2\)

Sum of squares of natural numbers:

The sum of squares of first n natural numbers is given by:

\(\rm \displaystyle\sum_{k=1}^{n}k^2 = \left[\dfrac{n(n+1)(2n+1)}{6}\right]\)

 

Calculation:

The sum of cubes of the first 20 natural numbers is given by:

\(\begin{align*} \left[\dfrac{n(n+1)}{2}\right]^2 &= \left[\dfrac{20(20+1)}{2}\right]^2\\ &= (210)^2\\ &=44100 \end{align*}\)

Similarly, the sum of squares of the first 20 natural numbers is given by:

\(\begin{align*} \left[\dfrac{n(n+1)(2n+1)}{6}\right] &= \dfrac{20(20+1)(40+1)}{6}\\ &= \dfrac{20\times 21\times41}{6}\\ &= 2870 \end{align*}\)

Therefore, sum of cubes of the first 20 natural numbers is 44100 and that of squares of the first 20 natural numbers is 2870.

Thus only the second statement is correct.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...