Question

Find the sum of 729-243+81.......... -1/3
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Answer 1

Answer:

the answer is 567 okay thanks

Answer 2

Answer:

1640 / 3

Step-by-step explanation:

Given---> 729 - 243 + 81 ...................- (1/3)

To find -----> Sum of given series

Solution----> ATQ,

729 - 243 +81 ...................... - ( 1/3 )

First we find series has how many terms,it is a GP

a = 729 , r = -243 / 729 = - 1 / 3 , aₙ = 1 / 3

aₙ = arⁿ⁻¹

=> 1/3 = ( 729 ) ( -1 / 3 )ⁿ⁻¹

=> 1 / ( 3 × 729 ) = ( -1 / 3 )ⁿ⁻¹

=> 1 / 2187 = ( -1 / 3 )ⁿ⁻¹

=> ( -1 / 3 )⁷ = ( -1 / 3 )ⁿ⁻¹

Comparing exponent we get,

=> 7 = n - 1

=> n = 7 + 1

=> n = 8

Now we find sum of 8terms

sₙ = a ( 1 - rⁿ ) / ( 1 - r )

S₈ = 729 { 1 - ( -1/3 )⁸ } / { 1 - ( - 1 / 3 ) }

= 729 { 1 - ( 1 / 6561 ) } /( 1 + 1/3 )

= 729 { ( 6561 - 1 ) / 6561 } / { (3 + 1 ) / 3 }

= ( 6560 / 9 ) / 4 / 3

= 6560 × 3 / 9 × 4

= 1640 / 3