Question

Find the unit palce of the following
1^3+2^3+3^3+....... 18^3​

Answer 1

Answer:

1

Step-by-step explanation:

We know that:

$1^3 + 2^3 + 3^3 + \cdots + n^3 = (1 + 2 + 3 + \cdots + n)^2$

So $1^3 + 2^3 + 3^3 + \cdots + 18^3 = (1 + 2 + 3 + \cdots + 18)^2$

We know that the sum of $1$ to $n$ is $\dfrac{n(n+1)}{2}$.

So $1 + 2 + 3 + \cdots + 18 = \dfrac{18\times 19}{2} = 9 \times 19 = 171$.

$1^3 + 2^3 + 3^3 + \cdots + 18^3 = 171^2$

The unit's digit of a square will always be $1$ if the unit's digit of the original number is $1$.

Thus, we conclude that the units digit of

$1^3 + 2^3 + 3^3 + \cdots + 18^3 = 1$.

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