Sum of Squares Formula The sum of the first n square numbers is equal to: n(n + 1)(2n + 1) / 6 The sum of consecutive square numbers from n12to n22is equal to: n12+ (n1+ 1)2+ ... + n22= n2(n2+ 1)(2n2+ 1) / 6 - n1(n1- 1)(2n1- 1) / 6 ...
Sum of Cubes Formula The sum of the first n cubes is equal to: n2(n + 1)2/ 4 The sum of consecutive cubic numbers from n13to n23is equal to: n13+ (n1+ 1)3+ ... + n23= n22(n2+ 1)2/ 4 - n12(n1- 1)2/ 4
This paper discusses the Sums of Squares of "m" consecutive Woodall Numbers. These discussions are made from the definition of Woodall numbers. Also learn the comparability of Woodall numbers and other special numbers. An attempt to communicate the formula for the sums of squares of 'm'...
In his work "On Spirals",Archimedes(287 – 212 BC) derived the formula for calculating the sum of consecutive perfect squares. Figure 1 shows the geometric representation of the sum used by Archimedes. He was able to derive the formula Explain Archimedes’ proof of the sum of consecutive perf...
Find the square of a sum equivalent to the expression below: {eq}(a+b)^2 {/eq} Square of a Sum: We can evaluate the product of two factors being sums of two variables using various ways. Some of it is known as the FOIL method and the Parrot's Beak method. All of wh...
The sum of the squares of three consecutive positive integers is 194. What are the three consecutive positive numbers? Quadratic Equations An equation with the power of 2 is called a quadratic equation. Such equations are solved using two main meth...
1) sum of squares 平方和 1. We prove that if 9 divides k or k is divisible by a prime q (q= ± 5 (mod 12)), then thesum of squaresof any k consecutive positive integers cannot be a nth power of prime (n ∈ N). 对给定的正整数k,证明了:当9|k或q|k(q=±5(mod 12)是一...
Sum of cubes formula of a polynomial is an essential formula in algebra. Click now to learn how to factor or find the sum of two cubes using solved example question at BYJU'S.
NCERT solutions for CBSE and other state boards is a key requirement for students. Doubtnut helps with homework, doubts and solutions to all the questions. It has helped students get under AIR 100 in NEET & IIT JEE. Get PDF and video solutions of IIT-JEE Mains & Advanced previous year pap...
To solve the problem step by step, we will follow the given information about the arithmetic progression (A.P.) and derive the necessary values.Step 1: Define the Terms of the A.P. Let the five consecutive terms of the A.P. be: