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Ex 9.3, 24 - Show ratio of sum of n terms of GP, sum from - Geometric Progression(GP): Calculation based/Proofs

Ex 9.3, 24 - Chapter 9 Class 11 Sequences and Series - Part 2
Ex 9.3, 24 - Chapter 9 Class 11 Sequences and Series - Part 3

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We need to show ratio of the sum of n terms of GP & sum of terms from (n + 1)th to 2nth term i.e. we need to calculate ( )/( ( + 1) (2 ) ) Putting values from (1) & (2) = (( a(1 ^ ))/((1 r)))/(( a)/((1 r))( ^ ^2 )" " ) = (( a(1 ^ ))/((1 r)))/(( a)/((1 r) ) ^ (1 ^ )" " ) = (( a(1 ^ ))/((1 r)))/ (( a(1 ^ ))/((1 r))) = ( a(1 ^ ))/(rn(1 ^ )) ( 1 r)/(1 r) Ex 9.3, 24 Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n+1)th to (2n)th term is ( 1)/rn Ex 9.3, 24 Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n+1)th to (2n)th term is ( 1)/rn We need to show ratio of the sum of n terms of GP & sum of terms from (n + 1)th to 2nth term i.e. we need to calculate ( )/( ( + 1) (2 ) ) Putting values from (1) & (2) = (( a(1 ^ ))/((1 r)))/(( a)/((1 r))( ^ ^2 )" " ) = (( a(1 ^ ))/((1 r)))/(( a)/((1 r) ) ^ (1 ^ )" " ) = (( a(1 ^ ))/((1 r)))/ (( a(1 ^ ))/((1 r))) = ( a(1 ^ ))/(rn(1 ^ )) ( 1 r)/(1 r) = 1/

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