Question

26. The sum of 1+ 2 5 + 3 5^ 2 + 4 5^ 3 +... up to n terms is​

Answer 1

Answer:

Let S = 1 + 2/5 + 3/52 + 4/53+….n/5n-1 …(i)

S/5 = 1/5 + 2/52 + 3/53 + 4/54+….(n-1)/5n-1 + n/5n …(ii)

(i)-(ii)

4S/5 = 1 + 1/5 + 1/52+ 1/53 + …1/5n-1 – n/5n

= 1(1-(1/5)n/(1-⅕) – n/5n

4S/5 = (1-1/5n)/4/5 – n/5n

= [(5n-1)/(4.5n-1)] – n/5n

= (5n+1-4n-5)/(4.5n)

S = (5n+1-4n-5)/(16.5n-1)

= (5n+1 /16.5n-1) -(4n+5)/(16.5n-1)

= (52/16) – (4n+5)/(16.5n-1)

= (25/16) – (4n+5)/(16.5n-1)

Hence option (1) is the answer.

Step-by-step explanation:

Hope it will help you