Question 10 Find the sum to n terms in the geometric progression x^3, x^5, x^7... (if x ≠ ±1)
Class X1 - Maths -Sequences and Series Page 192
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x³ + x⁵ + x⁷ + ..........( if x≠ ± 1)
here,
first term ( a) = x³
and common ratio (r) = x⁵ /x³ = x²
use the formula,
S_n = a(rⁿ -1)/(r -1)
= x³{(x²)ⁿ -1}/(x² -1)
= x³(x²ⁿ -1)/(x² -1)
hence,
sum of n terms of this series = x³ (x²ⁿ-1)(x²-1)
here,
first term ( a) = x³
and common ratio (r) = x⁵ /x³ = x²
use the formula,
S_n = a(rⁿ -1)/(r -1)
= x³{(x²)ⁿ -1}/(x² -1)
= x³(x²ⁿ -1)/(x² -1)
hence,
sum of n terms of this series = x³ (x²ⁿ-1)(x²-1)
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