Question

9. Sum to n terms:
(i) 0.7 + 0.77 + 0.777 +​

Answer 1

Step-by-step explanation:

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

7/9((1-.1) + (1-.01)+ (1-.001) +...n terms)

7/9(1-.1 + 1-(0.1)² + 1-(0.1)³+...n terms)

7/9((1+1+..n terms)- (.1+.1²+.1³+....+.1ⁿ))

.1+.1²+.1³+....+.1ⁿ is gp with a=.1, r=.1

sum= a(1-rⁿ)/ (1-r)

=.1(1-.1ⁿ)/1-.1 =1-0.1ⁿ/9

= 7/9( n - (1-0.1ⁿ)/9)

=7n/9 - 7/81 +7×0.1ⁿ/81