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ICSE Class 10 Answered

find the sum of the sequence 2-6+18........
Asked by suneelmsc | 27 Apr, 2020, 12:21: PM
Expert Answer
To find the sum of the sequence 2-6+18...
2-6+18-54+162-486+1458...
= (2+18+162+1458+...) - (6+54+486+...)
= 2(1+9+81+729+...) - 6(1+9+81+...)
= 2(1+9+92+93+...) - 6(1+9+92+93+...)
= -4(1+9+92+93+...)
1, 9, 92, 93, ... forms a G.P. with first term a = 1 and common ratio r = 9
Since the G.P. is infinite and r=9>1
Hence, the sum of the sequence 2-6+18... is -infinity.
Answered by Renu Varma | 27 Apr, 2020, 02:48: PM

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