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if an= -2/(4n^2)-(16n)+(15), [(4n^2)-(16n)+(15) dis entire thing is the denominator)] then: opt a) a1+a2+....+a10= 20/51 opt b) a1+a2+.....a10=30/51 opt c) a1+a2+......a25=50/141 opt d) a1+a2+.....a25=60/141 Its more than one ans type q, pls tell me a detailed explanation on how to do it as i din understand

Asked by joanmaria916 | 08 Jul, 2023, 04:37: PM

Expert Answer

TO find the sum of first 10 terms when a_n = -2/(4n² - 16n + 15)

4 straight n squared minus 16 straight n plus 15 equals 4 straight n squared minus 10 straight n minus 6 straight n plus 15 equals 2 straight n left parenthesis 2 straight n minus 5 right parenthesis minus 3 left parenthesis 2 straight n minus 5 right parenthesis equals left parenthesis 2 straight n minus 5 right parenthesis left parenthesis 2 straight n minus 3 right parenthesis rightwards double arrow straight a subscript straight n equals fraction numerator negative 2 over denominator left parenthesis 2 straight n minus 5 right parenthesis left parenthesis 2 straight n minus 3 right parenthesis end fraction equals negative open square brackets fraction numerator 1 over denominator 2 straight n minus 5 end fraction minus fraction numerator 1 over denominator 2 straight n minus 3 end fraction close square brackets equals fraction numerator 1 over denominator 2 straight n minus 3 end fraction minus fraction numerator 1 over denominator 2 straight n minus 5 end fraction straight a subscript 1 equals fraction numerator 1 over denominator negative 1 end fraction minus fraction numerator 1 over denominator negative 3 end fraction comma space straight a subscript 2 equals 1 over 1 minus fraction numerator 1 over denominator negative 1 end fraction comma space straight a subscript 3 equals 1 third minus 1 over 1 comma straight a subscript 4 equals 1 fifth minus 1 third comma... straight a subscript 10 equals 1 over 17 minus 1 over 15 rightwards double arrow straight a subscript 1 plus straight a subscript 2 plus straight a subscript 3 plus... plus straight a subscript 10 equals negative 1 plus 1 third plus 1 plus 1 plus 1 third minus 1 plus 1 fifth minus 1 third plus... plus 1 over 17 minus 1 over 15 space space space space space equals 1 third plus 1 over 17 space space space space space equals 20 over 51

Answered by Renu Varma | 13 Jul, 2023, 12:06: PM

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if an= -2/(4n^2)-(16n)+(15), [(4n^2)-(16n)+(15) dis entire thing is the denominator)] then: opt a) a1+a2+....+a10= 20/51 opt b) a1+a2+.....a10=30/51 opt c) a1+a2+......a25=50/141 opt d) a1+a2+.....a25=60/141 Its more than one ans type q, pls tell me a detailed explanation on how to do it as i din understand

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