# airthmetic progression

posted by .

prove that
mean of cubes of first n natural numbers is [n(n+1)(n+1)]/4

• airthmetic progression -

by induction, you can show that

n
∑ k^3 = n^2 * (n+1)^2 / 4
k=1

now divide by n, and you're done.

## Similar Questions

1. ### math

The sum of the first 5 natural numbers is 15 or (5)(6)/2. The sum of the first 21 natural numbers is 231=(21)(22)/2, and the sum of the first 30 numbers is 465. Use inductive reasoning to derive the formula for the sum of the first …
2. ### airthmetic progression

If m, n are natural numbers, m > n, sum of mth and nth term of an increasing AP is 2m and their product is m^2–- n^2, then what is the (m+n)th term of the A.P.?
3. ### airthmetic progression

If m, n are natural numbers, m > n, sum of mth and nth term of an increasing AP is 2m and their product is m^2–- n^2, then what is the (m+n)th term of the A.P.?
4. ### maths-Arithmetic progression

Prove that mean of squares of first n natural numbers is (n+1)(2n+1)/6
5. ### Algebra/Number Theory

In a sequence of four positive numbers, the first three are in geometric progression and the last three are in arithmetic progression. The first number is 12 and the last number is 452. The sum of the two middle numbers can be written …
6. ### math

The third,sixth and seventh terms of a geometric progression(whose common ratio is neither 0 nor 1) are in arithmetic progression. Prove dat d sum of d first three is equal to d fourth term
7. ### Michael

How many natural numbers are there with the property that they can be expressed as sum of cubes of two natural numbers in two different ways.
8. ### Permutation and combination

How many natural numbers are there with the property that they can be expressed as sum of cubes of two natural numbers in two different ways.
9. ### Maths

The numbers p,10 and q are 3 consecutive terms of an arithmetic progression .the numbers p,6 and q are 3 consecutive terms of a geometric progression .by first forming two equations in p and q show that p^2-20p+36=0 Hence find the …
10. ### algebra

The sum of the three numbers in Arithmetic Progression is 33. If the numbers are increased by 2, 1, and 6 respectively the new numbers will be in Geometric progression. Find these numbers.

More Similar Questions