Question

1+ 2 /7 + 3 /7^ 2 + 4 /7^ 3 +.......... Sum to n terms the series ​

Answer 1

Answer:

Step-by-step explanation:

1/7+2/7^2+1/7^3+2/7^4+...

Note that we can split this into two different sums

[1/7 + 1/7^3 +  1/7^5+......]  +  [ 2/7^2 + 2/7^4 + 2/7^6+....]

The sum of the first series =     [1/7] / [1 - 1/7^2 ]  = 7/48

And the sum of the second series  =  [ 2/7^2] / [ 1 - 1/7^2]  = 1/24

So.....the sum of the whole series =   7/48 + 1/24  =  7/48 + 2/48   =  9/48