1) 7The sum to infinity of1) 1/5+2) 7/243) 5/484) 3/16

1.	1) 7The sum to infinity of1) 1/5+2) 7/243) 5/484) 3/16
Answer» 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 = 3/16 hence, the correct option is (d)

Answer»

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 = 3/16

hence, the correct option is (d)

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