G.P series 7+7.7+7.77+7.777+...upto 50 terms
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Given:
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.
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.
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