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Find the sum of 1+(4/5)+(7/5^2)+(10/5^3)+........to n terms.

Find the sum of 1+(4/5)+(7/5^2)+(10/5^3)+........to n terms.

Grade:12

2 Answers

Pratik Tibrewal
askIITians Faculty 37 Points
7 years ago
given S = 1 + 4/5 + 7/ 5^2 + 10/5^3 + ... -------1
(1/5)S = 1/5+ 4/5^2 + 7/5^3 + ... --------------2
eqn 1 -eqn 2, gives

(4/5)S = 1 + 3/5 + 3/5^2 + 3/5^3 + ..........
4/5S = 1 + 3/5( 1 + 1/5 + 1/5^2 + ..... n - 1 terms) (a G.P. with n-1 terms, first term = 1, and common ration r = 1/5)

S = 5/4 ( 1 + 3/5( (1) ( (1/5)^(n-1) - 1)/(1/5-1)))


Thanks and Regards,

Pratik Tibrewal
askiitians faculty
BTech IITG
ankit singh
askIITians Faculty 614 Points
one year ago
iven S = 1 + 4/5 + 7/ 5^2 + 10/5^3 + ... -------1
(1/5)S = 1/5+ 4/5^2 + 7/5^3 + ... --------------2
eqn 1 -eqn 2, gives
 
(4/5)S = 1 + 3/5 + 3/5^2 + 3/5^3 + ..........
4/5S = 1 + 3/5( 1 + 1/5 + 1/5^2 + ..... n - 1 terms) (a G.P. with n-1 terms, first term = 1, and common ration r = 1/5)
 
S = 5/4 ( 1 + 3/5( (1) ( (1/5)^(n-1) - 1)/(1/5-1)))
 

 

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