Question

hi therecontent qualityFind the sum to $\mathsf{n}$ terms of the series $\mathsf{ 1 \: + \: \dfrac{3}{2} \: + \: \dfrac{5}{4} \: + \: \dfrac{7}{8}+.....}$.

Answer 1

Answer:

Step-by-step explanation:

Sum of the Terms of an Arithmetic Sequence (Arithmetic Series) To find the sum of the first terms of an arithmetic sequence use the formula, S n = n ( a 1 + a 2 ) 2 , where is the number of terms, is the first term and is the last term.

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 ☺