Question

find the sum of series : 7+77+777+......To n terms ​

Answer 1

Answer:

let try

7/9(9+99+999+.........n terms)

=7/9((10-1)+(100-1)+(1000-1)+.......... n terms)

=7/9((10+100+1000+......n terms)+(1+1+1.......n terms))

=7/9((10+100+1000+......n terms)-n)

here a=10 r=10

7/9(10(10n-1)/9-n)

Answer 2

Answer: (7/81)*(10ⁿ⁺¹ - 10 - n)

Step-by-step explanation:

Let S = 7+77+777+... n terms

S = 7(1+11+111..... n terms)

S = (7/9)*(9+99+999.... n terms)

S = (7/9)*((10-1) + (100-1) + (1000-1) + ..... nterms)

S = (7/9)*((10+100+1000+... n terms) - n)

Using Sum of G.P. formula....

S = (7/9)*[(10(10ⁿ - 1)/(10 - 1)) - n]

S = (7/9)*[(10(10ⁿ - 1)/9) - n]

S = (7/81)*(10ⁿ⁺¹- 10 - n)

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