Prove the following by the principle of mathematical induction: `7+77+777++777++\ ddotn-d igi t s7=7/(81)(10^(n+1)-9n-10)` for all `n in N `

Explanation

Let `P(n)` be the given statement

Now.

`P(n): 7+77+777+ldots+777 ldots n` dgne `quad ldots 7=frac{7}{81}(10^{kappa+1}-9 n-10)`

step(1)=

`P(1)=7=frac{7}{81}(10^{2}-9-10)=frac{7}{81} times 81`

Thus, `P(1)` is true.

Step 2:

Let `P(m)` be true .

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