Question

Sum of 11+101+1001...n ?

Answer 1

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Answer 2

Answer:

11+101+1001…+n = 109n-10/9

Step-by-step explanation:

First term             = 11
Last term             = n
Number of terms = x
11+ 101+ 1001+ ….+n    =  (10+1) + ( 100+1) + (1000+1)+... +n
i e, (10+100+1000+...+ n) + ( 1+1+1+...+ n)

10+100+1000+ ... +n  is in Geometric Progression (G.P)
First term (a) =10
Common Ratio ( r ) = 10
Equation,  Sn = a(rn - 1)/r-1
Sn = 10 (10n -1)/(10-1)
     = 10 (10n -1)/9
     = 10 (10n -1)/9
                 =10(10n -1)/9 + n
                 = (100n-10)/9+ 9n/9
                 =(100n-10+9n)/9
                 = 109n-10/9

Therefore,
11+101+1001…+n = 109n-10/9



To learn about variables:
brainly.in/question/40782849

To learn more about constant:
brainly.in/question/513544



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