Question

1^3+2^3+3^3+.......+k^3=16900 then find 1+2+3+.....K

Answer 1

Step-by-step explanation:

according to the question the answer will be 5360

Answer 2

1 + 2 + 3 + ........ + K = 130

Step-by-step explanation:

We have,

$1^3+2^3+3^3+.......+k^3$ = 16900          

To find, 1 + 2 + 3 + ........ + K = ?

We know that,

$1^3+2^3+3^3+.......+n^3=(\dfrac{n(n+1)}{2} )^2$ and

1 + 2 + 3 + ........ + n = $\dfrac{n(n+1)}{2}$

∴ $1^3+2^3+3^3+.......+k^3$ = 16900  

⇒ $(\dfrac{k(k+1)}{2} )^2$ = 16900

⇒ $(\dfrac{k(k+1)}{2} )^2$ = $130^2$

⇒ $\dfrac{k(k+1)}{2}$ = 130                 ......... (1)

∴ 1 + 2 + 3 + ........ + K

= $\dfrac{k(k+1)}{2}$ = 130

Thus, 1 + 2 + 3 + ........ + K = 130