Question

If 1^3 +2^3 + 3^3 + … + a^3 = 5041. Then find 1 + 2 + 3 + . . . +a.

1 point


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Answer 1

Given : 1³ + 2³ + 3³ + ...... + a³ = 5041

To find : 1 + 2 + 3 + ...... + a = ?

solution : we know,

1³ + 2³ + 3³ + 4³ + ..... + n³ = [n(n + 1)/2]²

also 1 + 2 + 3 + 4 + .......+ n = n(n + 1)/2

so, 1³ + 2³ + 3³ + ...... + a³ = [a(a + 1)/2]² ......(1)

and 1 + 2 + 3 + ..... + a = a(a + 1)/2 .....(2)

from equations (1) and (2) we get,

1³ + 2³ + 3³ + ...... + a³ = (1 + 2 + 3 + ... + a)²

⇒5041 = (1 + 2 + 3 + .... + a)²

⇒1 + 2 + 3 + .... + a = √5041 = 71

Therefore value of 1 + 2 + 3 + .... + a = 71

Answer 2

Value of 1 + 2 + 3 + .... + a = 71

Step-by-step explanation:

Given: 1³ + 2³ + 3³ + ...... + a³ = 5041

Find: Value of 1 + 2 + 3 + ...... + a

Solution:

Formula for summation are as follows:

1³ + 2³ + 3³ + 4³ + ..... + n³ = [n(n + 1)/2]²

1 + 2 + 3 + 4 + .......+ n = n(n + 1)/2

Given that 1³ + 2³ + 3³ + ...... + a³ = 5041.

It can also be written as:

1³ + 2³ + 3³ + ...... + a³ = [a(a + 1)/2]² ---------------(1)

1 + 2 + 3 + ..... + a = a(a + 1)/2 ---------------(2)

Substituting equation (2) in (2), we get:

1³ + 2³ + 3³ + ...... + a³ = (1 + 2 + 3 + ... + a)²

5041 = (1 + 2 + 3 + .... + a)²

So (1 + 2 + 3 + .... + a) = √5041 = 71