Here's a very easy and clean copyable answer without any formulas. Step-by-step and simple:

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Given Series:

1/11 + 11/11² + 111/11³ + 1111/11⁴ + ...

Step 1: Observe the pattern:

Numerators:

1, 11, 111, 1111, ...

Denominators:

11, 121, 1331, 14641, ... (powers of 11)

Let’s rewrite each term:

1st term  =   1 / 11
2nd term  =  11 / 121      = 1 / 11
3rd term  = 111 / 1331     ≈ 0.0834
4th term  = 1111 / 14641   ≈ 0.0759

Hard to add directly — but observe:

Each numerator is like:

1 =        1
11 =      10 + 1
111 =    100 + 10 + 1
1111 =  1000 + 100 + 10 + 1

So we rewrite the whole series as:

(1/11) 
+ (10/121 + 1/121) 
+ (100/1331 + 10/1331 + 1/1331) 
+ ...

Now group terms:

= (1/11) + (1/121) + (10/121) 
  + (1/1331) + (10/1331) + (100/1331) 
  + ...

Rewriting all together:

= (1/11 + 1/121 + 1/1331 + ...) 
+ (10/121 + 10/1331 + 10/14641 + ...) 
+ (100/1331 + 100/14641 + ...) 
+ ...

Now, this becomes a neat sum of geometric series.

Each group is a geometric series and their sum leads to:

Final answer = 11/10

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✅ Final Answer: 11/10 or 1.1

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👉 You can copy and paste this explanation anywhere without issues.
If you want the same in Telugu, just tell me.