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CBSE Class 12-science Answered

 If Sn  represents the sum to n terms of a GP whose first term & common ratio are a & r resp then find the  value of S1 + S3 + S5 + ..... + S2n-1 
Asked by rushabhjain.avv | 02 Nov, 2019, 10:23: PM
answered-by-expert Expert Answer
W e space k n o w space t h a t space S subscript n equals fraction numerator a left parenthesis r to the power of n minus 1 right parenthesis over denominator left parenthesis r minus 1 right parenthesis end fraction
U sin g space t h e space a b o v e space f o r m u l a comma space w e space h a v e
S subscript 1 plus S subscript 3 plus S subscript 5 plus... plus S subscript 2 n minus 1 end subscript
equals a fraction numerator open parentheses r minus 1 close parentheses over denominator left parenthesis r minus 1 right parenthesis end fraction plus fraction numerator a left parenthesis r cubed minus 1 right parenthesis over denominator left parenthesis r minus 1 right parenthesis end fraction plus..... plus fraction numerator a left parenthesis r to the power of 2 n minus 1 end exponent minus 1 right parenthesis over denominator left parenthesis r minus 1 right parenthesis end fraction
equals fraction numerator a over denominator r minus 1 end fraction open square brackets left parenthesis r minus 1 right parenthesis plus left parenthesis r cubed minus 1 right parenthesis plus.... plus left parenthesis r to the power of 2 n minus 1 end exponent minus 1 right parenthesis close square brackets
equals fraction numerator a over denominator r minus 1 end fraction open square brackets r plus r cubed plus... plus r to the power of 2 n minus 1 end exponent minus n close square brackets
equals fraction numerator a over denominator r minus 1 end fraction open square brackets r open parentheses 1 plus r squared plus... plus r to the power of 2 n end exponent close parentheses minus n close square brackets
equals fraction numerator a over denominator r minus 1 end fraction open square brackets r open parentheses fraction numerator open parentheses r squared close parentheses to the power of n minus 1 over denominator r squared minus 1 end fraction close parentheses minus n close square brackets
equals fraction numerator a over denominator r minus 1 end fraction open square brackets r open parentheses fraction numerator r to the power of 2 n end exponent minus 1 over denominator r squared minus 1 end fraction close parentheses minus n close square brackets
Answered by Renu Varma | 04 Nov, 2019, 10:38: AM
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