What is the sum of the first 555 terms of the geometric series 1,23,49 ...?1,23,49 ...?1,23,49 ...?
Answer:
211812118121181
- The sum of first nnn terms of a G.P.G.P.G.P. is given by,
Sn=a(1−rn)(1−r)Sn=a(1−rn)(1−r)Sn=a(1−rn)(1−r)
Here, the first term, a=1a=1a=1 and
the common ratio, r=ak+1ak where k≥1r=ak+1ak where k≥1r=ak+1ak where k≥1
⟹r=231=23⟹r=231=23⟹r=231=23 - The sum of first nnn terms of this G.P.G.P.G.P. is given by,
[Math Processing Error] Now, the sum of the first 55 terms of the G.PG.P is given by, [Math Processing Error] - Hence, the sum of the first 55 terms of the G.P.G.P. is 2118121181.