For what value of $n$, the sum of digits in the number $(10^n + 1)$ is 2?
For what value of $n$, the sum of digits in the number $(10^n + 1)$ is 2?
For $n = 0$ only
For any whole number $n$
For any positive integer $n$ only
For any real number $n$
Solution
For any whole number $n$, $10^n$ is 1 followed by $n$ zeros, so $10^n + 1$ has digit sum $1 + 1 = 2$ (e.g. $n=0$: 2; $n=1$: 11; $n=2$: 101 — each has digit sum 2). It holds for all whole numbers $n$ (including 0). For non-integer real $n$ the expression is not such an integer. Hence: for any whole number $n$.