Find the sum of the series N - 1 - 3- 1 - 1 5 - 1 - 35 - 1 0 0 termsA- 99 - 199B- 1 - 199C- 1 0 0 - 2 0 1D- 1 - 201E- 1 - 199

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Question

Find the sum of the series N= 1/3 + 1/15 + 1/35………… 100 terms

99/199

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1/199

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100/201

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1/201

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1/199

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Solution

The correct option is C 100/201
First term of the series (1/3) = 1/(3x1)= 1/2[1-1/3]

Second term of the series (1/15) = 1/(3x5)=1/2[1/3-1/5]

Third term of the series (1/35) = 1/(7x5)=1/2[1/5-1/7]

..............................................................................

100th term of the series (1/199 x 201) = 1/2[1/199 - 1/201]

1/2[1-1/3+1/3-1/5+1/5-1/7+1/7………………………………………+1/199-1/201]

½[1-1/201]= 200/(2x201)=100/201

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