Find the value of 1 + 2/3 - 2/4 + 2/5 + ...... to infinite is :

Asked by arijitdas1908 | 4th Apr, 2020, 02:09: PM

Expert Answer:

1+2/3-2/4+2/5-2/6+......to infinity
equals 1 plus 2 open parentheses 1 third minus 1 fourth plus 1 fifth minus 1 over 6 plus..... close parentheses
equals 1 plus 2 open square brackets negative 1 plus 1 half plus open parentheses 1 minus 1 half plus 1 third minus 1 fourth plus 1 fifth minus 1 over 6 plus..... close parentheses close square brackets
equals 1 plus 2 open square brackets negative 1 half plus open parentheses 1 minus 1 half plus 1 third minus 1 fourth plus 1 fifth minus 1 over 6 plus..... close parentheses close square brackets
equals 1 minus 1 plus 2 open parentheses 1 minus 1 half plus 1 third minus 1 fourth plus 1 fifth minus 1 over 6 plus..... close parentheses
equals 2 open parentheses 1 minus 1 half plus 1 third minus 1 fourth plus 1 fifth minus 1 over 6 plus..... close parentheses
straight S subscript 1 equals 1 minus 1 half plus 1 third minus 1 fourth plus 1 fifth minus 1 over 6 plus.....
equals open parentheses 1 plus 1 third plus 1 fifth plus..... close parentheses minus open parentheses 1 half plus 1 fourth plus 1 over 6 plus...... close parentheses equals straight m minus straight n
straight m equals open parentheses 1 plus 1 third plus 1 fifth plus..... close parentheses space space and space space
straight n equals 1 half plus 1 fourth plus 1 over 6 plus.....
equals 1 half open parentheses 1 plus 1 half plus 1 third plus..... close parentheses
equals 1 half open square brackets open parentheses 1 plus 1 third plus 1 fifth plus..... close parentheses plus open parentheses 1 half plus 1 fourth plus 1 over 6 plus.... close parentheses close square brackets
equals 1 half open parentheses straight m plus straight n close parentheses
rightwards double arrow 1 half straight n equals 1 half straight m space rightwards double arrow space straight m equals straight n
rightwards double arrow straight S subscript 1 equals 0
Hence comma space 1 plus 2 over 3 minus 2 over 4 plus 2 over 5 minus 2 over 6 plus.... space to space infinity space equals space 0

Answered by Renu Varma | 5th Apr, 2020, 04:13: PM

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