Question

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Answer 1

Answer:

1/1 + 3/2 + 5/4 + 7/8 + 9/16 + 11/32 + …

= (1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + …)

plus 2(1/2 + 1/4 + 1/8 + 1/16 + 1/32 + …)

plus 2(1/4 + 1/8 + 1/16 + 1/32 + …)

plus 2(1/8 + 1/16 + 1/32 + …)

plus…

= 2 + 2(1) + 2(1/2) + 2(1/4) + 2(1/8) + …

= 2 + 2(1 + 1/2 + 1/4 + 1/8 + …)

= 2 + 2(2)

= 6

Answer 2

This series is at first converted into an AGP,that is,an arithmetico-geometric progression,where one part of term is in AP,and other part is in GP.

A formula is given in attachment for calculating sum of AGP series.

a is first term of AP,b is first term of GP,d is common difference of AP and r is common ratio of GP.

Values are substituted and we get the answer.

And for infinite AGP, r^n is equal to 0.That is also mentioned in attachment.

Hope you understood ☺