Question

Sn= 6+66+666+6666+....

Answer 1

Answer:

6(1+11+111+…………..n)

=6*(9/9)(1+11+111+…………..n)

=(6/9)(9+99+999………….n)

now,

=(6/9)((10–1)+(100–1)+(1000–1)………..n)

=(6/9)[(10+100+1000…….n)-(1+1+1……..n)]

=(6/9)[(10+10^2+10^3………n) - (1+1+1……..n)]

now this is in Geometric progression.

r = 10

a=10

now put in the formula

Sn= a(r^n-1)/r-1

=10(10^n-1)/9

So,

Sn = (6/9)[(10(10^n-1)/(10–1))- n]

= (2/3)[10(10^n-1)/9 - n]

Answer 2

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