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ICSE Class 10 Answered

find the sum of the series  1+(1+x)+(1+x+x^2)+..........to n terms, x not equal to 1  
Asked by tarunkumardas32 | 17 Jul, 2019, 04:10: PM
answered-by-expert Expert Answer
1 plus left parenthesis 1 plus x right parenthesis plus left parenthesis 1 plus x plus x squared right parenthesis plus.... t o space n space t e r m s equals fraction numerator x minus 1 over denominator x minus 1 end fraction plus fraction numerator x squared minus 1 over denominator x minus 1 end fraction plus fraction numerator x cubed minus 1 over denominator x minus 1 end fraction plus... plus fraction numerator x to the power of n minus 1 over denominator x minus 1 end fraction equals fraction numerator x plus x squared plus x cubed plus... plus x to the power of n minus n over denominator x minus 1 end fraction equals fraction numerator begin display style fraction numerator x left parenthesis x to the power of n minus 1 right parenthesis over denominator x minus 1 end fraction end style minus n over denominator x minus 1 end fraction equals fraction numerator x left parenthesis x to the power of n minus 1 right parenthesis minus n left parenthesis x minus 1 right parenthesis over denominator left parenthesis x minus 1 right parenthesis squared end fraction
Answered by Renu Varma | 18 Jul, 2019, 09:49: AM

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