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        Find the sum of tens to infinity 1+2/4+2/4.5/8+2/4.5/8.8/12+.......... Infinity
one year ago

							Concept : Binomial expansion of rational indexLet S = 1+2/4+2/4.5/8+2/4.5/8.8/12+.......... Assume S to be (1 + x)n = 1 + nx + n(n – 1)x2 / 2!+ ….......... ,  |x| So nx = 2/4 = 1/2 ,  n(n – 1)x2 / 2! = 2/4.5/8 = 5/16  or  n(n – 1)x2 = 5/8n2(n – 1)x2 / n = 5/8  => (n – 1)(nx)2 = 5n/8  => (n – 1)(1/4) = 5n/82n – 2 = 5n   =>  n = – 2/3 x = – 3/4|x| = 3/4 th term of S.Therefore, our assumption is correct. S = (1 – 3/4)– 2/3 = (1/4) – 2/3   S = 42/3

one year ago
							Concept : Binomial expansion of rational indexLet S = 1+2/4+2/4.5/8+2/4.5/8.8/12+.......... Assume S to be (1 + x)n = 1 + nx + n(n – 1)x2 / 2!+ ….......... ,  |x| So nx = 2/4 = 1/2 ,  n(n – 1)x2 / 2! = 2/4.5/8 = 5/16  or  n(n – 1)x2 = 5/8n2(n – 1)x2 / n = 5/8  => (n – 1)(nx)2 = 5n/8  => (n – 1)(1/4) = 5n/82n – 2 = 5n   =>  n = – 2/3 x = – 3/4|x| = 3/4 Also the values of n & x satisfy 4th term of S.Therefore, our assumption is correct. S = (1 – 3/4)– 2/3 = (1/4) – 2/3   S = 42/3

one year ago
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