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If if a1 a2 a3 are in ap then (a2n+1-a1/a2n+1+a1)+(a2n-a2/a2n+a2)+.......(an+2-an/an+2+an) is equal to
Asked by shritejpatil182 | 31 May, 2019, 09:33: AM
answered-by-expert Expert Answer
a subscript 1 comma space a subscript 2 comma space... comma space a subscript 2 n plus 1 end subscript space a r e space i n space A. P rightwards double arrow a subscript 2 n plus 1 end subscript equals a subscript 1 plus 2 n d comma space a subscript 2 n end subscript equals a subscript 1 plus left parenthesis 2 n minus 1 right parenthesis d comma space.... comma space a subscript 2 equals a subscript 1 plus d rightwards double arrow a subscript 2 n plus 1 end subscript minus a subscript 1 equals 2 n d comma space a subscript 2 n plus 1 end subscript plus a subscript 1 equals 2 a subscript 1 plus 2 n d comma space a subscript 2 n end subscript minus a subscript 2 equals comma space a subscript 2 n end subscript minus a subscript 2 equals 2 a subscript 1 plus 2 n d space a n d space s o space o n C o n s i d e r comma fraction numerator a subscript 2 n plus 1 end subscript minus a subscript 1 over denominator a subscript 2 n plus 1 end subscript plus a subscript 1 end fraction plus fraction numerator a subscript 2 n end subscript minus a subscript 2 over denominator a subscript 2 n end subscript plus a 2 end fraction plus fraction numerator a subscript 2 n minus 1 end subscript minus a subscript 3 over denominator a subscript 2 n minus 1 end subscript plus a subscript 3 end fraction plus... plus fraction numerator a subscript n plus 2 end subscript minus a subscript n over denominator a subscript n plus 2 end subscript plus a subscript n end fraction equals fraction numerator 2 n d over denominator 2 a subscript 1 plus 2 n d end fraction plus fraction numerator left parenthesis 2 n minus 2 right parenthesis d over denominator 2 a subscript 1 plus 2 n d end fraction plus... plus fraction numerator 2 d over denominator 2 a subscript 1 plus 2 n d end fraction equals fraction numerator n d over denominator a subscript 1 plus n d end fraction plus fraction numerator left parenthesis n minus 1 right parenthesis d over denominator a subscript 1 plus n d end fraction plus... plus fraction numerator d over denominator a subscript 1 plus n d end fraction equals fraction numerator d left parenthesis 1 plus 2 plus 3 plus... plus n right parenthesis over denominator a subscript 1 plus n d end fraction equals fraction numerator d begin display style fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 end fraction end style over denominator a subscript 1 plus n d end fraction equals fraction numerator n left parenthesis n plus 1 right parenthesis d over denominator 2 a subscript n plus 1 end subscript end fraction equals fraction numerator n left parenthesis n plus 1 right parenthesis left parenthesis a subscript 2 minus a subscript 1 right parenthesis over denominator 2 a subscript n plus 1 end subscript end fraction
Answered by Renu Varma | 31 May, 2019, 10:31: AM

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