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If the sum to infinity of the series :- 1 +4x + 7x 2 + 10x 3 ...infinite = 35/16. Find x?

If the sum to infinity of the series :-
1 +4x + 7x2 + 10x3...infinite = 35/16. Find x?

Grade:11

1 Answers

Ajay Verma
askIITians Faculty 33 Points
9 years ago
solution:

S =1 +4x + 7x2+ 10x3.......infinite.......................(1)
xS = x + 4x2+ 7x3.................. infinite....................(2)

eqn1 – eqn2 =
(1 – x)S = 1 + 3x + 3x2+ 3x2…...............infinite

(1 – x)S = 1 + 3 { x + x2+ x3+ …........... infinite}........ (3)
this is a G.P. of common ratio = x
so... using sum of G.P. = a/ (1-r)
here... a = first term andr = common ratio

so
(1 – x)S = 1 + 3 x/ (1 – x)
given S = 35/16

so
(1- x) 35/16 = 1 +3 x/ (1 – x)
(1 – x)235 = 16 (1- x) + 48x
solving..

35x2+ 32x -19 = 0

solve this quadratic eqn to get the answer..

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