Question

7 + 7.7 + 7.77 + 7.777 +...... find the sum to n terms

Answer 1

Answer:

Step-by-step explanation:

7+7.7+7.77+7.777+....upto 50 terms

Taking 7 common,

7 (1+1.1+1.11+1.111+......50 terms)

Multiplying 9 inside the bracket & dividing by 9,

7/9 (9 + 9.9 + 9.99+ 9.999......50 terms)

7/9 ( (10-1) + (10-0.1) + (10-0.01).......50 terms)

Taking 10 common,

7 x 10 /9 ( 50 - (1+0.1+0.01+.......50 terms))

the terms (1+0.1+0.01+.....50 terms) are in GP serier with common ratio r = 0.1,

70/9 ( 50 - [1 (1 - (0.1)^50)]/1-0.1)

is the sum of series.