3 - Sequence and Series Questions Answers

Find Sum to n terms 

 

x/1-x²  +  x²/1-x⁴  +  x⁴/1-x⁸ + ....

Asked By: LUFFY
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Joshi sir comment

x1-x2=11-x-11-x2 break all terms similarly and solve 

The sum of three positive real numbers x, y and z is 9. If the largest positive difference between any 2 of the 3 numbers is 5 and these 3 numbers are in arithmetic progression then the product of these 3 numbers will be what .please tell me.

Asked By: S.NANDHINI
is this question helpfull: 8 2 read solutions ( 1 ) | submit your answer
Joshi sir comment

let the numbers are a-d, a, a+d

then according to the given condition    a-d+a+a+d = 9   so  3a = 9   so a = 3

and [a+d]-[a-d] = 5   so 2d = 5 so d =5/2

now solve 

 

The AM of two positive numbers a & b exceeds their GM by 3/2 & the GM exceeds the HM by 6/5 such that a+b= α , |a-b|=β , then which of them are correct,

1) α + β² = 96            2) α + β² =74          3)α²+β = 234         4)α²+β = 84 

Asked By: AMIT DAS
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Joshi sir comment

(a+b)/2 = √ab + 3/2                   (1)                        or         a+b = 2√ab + 3

√ab      = 2ab/(a+b)  +  6/5       (2)                        or         5(a+b)√ab  =  10ab + 6(a+b)      

on solving these 2 we get               5[2√ab + 3]√ab = 10ab + 6[2√ab + 3]

                                           or               10ab + 15√ab  =  10ab + 12√ab + 18

                                           or                3√ab = 18     or      ab = 36          and      a+b = 15 = α

 so a-b = √(225 - 144)     =    √81     =     9 = β

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