Solution: Let ‘a’ be the first term of GP and ‘r’ be the common ratio. We know that nth term of a GP is given by- an = arn-1 As, a = 4 (given) And a5 – a3 = 32/81 (given) 4r4 – 4r2 = 32/81 4r2(r2 –...
Solution: We can write 0.125125125 as 0.125125125 = 0.125 + 0.000125 + 0.000000125 + … This can be written as $ 125/{{10}^{3}}~+\text{ }125/{{10}^{6}}~+\text{ }125/{{10}^{9}}~+\text{ }\ldots $...
Solution: Given: Sp = 1 + rp + r2p + … ∞ By using the formula, S∞ = a/(1 – r) Where, a = 1, r = rp So, Sp = 1 / (1 – rp) Similarly, sp = 1 – rp + r2p – … ∞ By using the formula, S∞ = a/(1 – r)...
Solution: We can write the LHS of above equation as: ${{2}^{1/4}}~.\text{ }{{2}^{2/8}}~.\text{ }{{2}^{3/16}}~.\text{ }{{2}^{1/8}}~\ldots \text{ }\infty $ ${{2}^{1/4\text{ }+\text{ }2/8\text{...
Solution: Let us take the LHS first: We can write the given equation as: 91/3 + 1/9 + 1/27 + …∞ So let us take $ m\text{ }=\text{ }1/3\text{ }+\text{ }1/9\text{ }+\text{ }1/27\text{ }+\text{ }\ldots...
(iii) 2/5 + 3/52 + 2/53 + 3/54 + …. ∞ (iv) 10 – 9 + 8.1 – 7.29 + …. ∞ Solution: (iii) 2/5 + 3/52 + 2/53 + 3/54 + …. ∞ We can write the given terms as, (2/5 + 2/53 + …) + (3/52 + 3/54 + …) where (a =...
(i) 1 – 1/3 + 1/32 – 1/33 + 1/34 + … ∞ (ii) 8 + 4√2 + 4 + …. ∞ Solution: (i) 1 – 1/3 + 1/32 – 1/33 + 1/34 + … ∞ We are given that: S∞ = 1 – 1/3 + 1/32 – 1/33 + 1/34 + … ∞ On comparing with the...