Question
What is the ratio of the sum of the squares of the first
8 natural numbers to the sum of the first 12 odd natural numbers?Solution
Sum of first 'n' odd numbers = n2
Sum of square of first 'n' natural numbers. =Â {(n x (n + 1) x (2n + 1)}/6
ATQ
Sum of square of first 8 natural numbers = {8 X ([8 + 1) X (8 X 2 + 1) ] ÷ 6} = [(8 X 9 X 17) ÷ 6] = 204
Sum of first 12 odd natural numbers = n2Â = 122Â = 144
Required ratio = (204/144) = 17:12
Who was appointed as the new Managing Director (MD) and Chief Executive Officer (CEO) of Axis Capital?
On Mahaparinirvan Day in December 2023, where was a wax figure of the architect of the Constitution, Baba Saheb Ambedkar, unveiled in a wax museum?
In which country the 12th edition of the 'World Hindi Conference' is being held?
India won its first-ever men’s compound archery World Championship gold in 2025 by defeating which country in the final?Â
Which group of workers is eligible for NAMASTE scheme, which is also a key aspect of the banking industry's financial inclusion initiatives?
What is the primary goal of the joint venture between Coal India Limited (CIL) and GAIL for setting up a Coal to Synthetic Natural Gas (SNG) plant?
What was the total value of Direct Benefit Transfers (DBT) routed through PMJDY accounts in 2024–25?
Which year Indian stamp Act came ?
What unique support will Indian athletes have at the Paris Olympics?
Which bank recently became the first in 11 years to receive an ‘in-principle’ universal bank licence from the RBI?
Relevant for Exams:
