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If H1,H2,H3.........H20 be 20 harmonic means between 2 and 3 then H1+2/H1-2 + H20+3/H20-3=????

If H1,H2,H3.........H20 be 20 harmonic means between 2 and 3 then H1+2/H1-2 + H20+3/H20-3=????

Grade:11

2 Answers

aftab alam
13 Points
4 years ago
d=(1/b-1/a)/n+1=(1/3-1/2)/20+1=-1/126
1/H1=1/a+d=1/2-1/126=62/126
H1=126/62
1/H20=1/a+20*d=1/2+20*(-1/126)=43/126
H20=126/43
now,H1+2/H1-2=(126/62+2)/(126/62-2)=125
H20+3/H20-3=(126/43+3)/(126/43-3)=-85
finally,125+(-85)=40 ans
Hrutika
13 Points
11 months ago
We know that,
13=12+21dd=16×21     (1)
Now, given 
H1+2H12+H20+3H203=12+1H1121H1+13+1H20131H20
=12+12+d12d12+13+13d1313+d(1H1=12+d,  1H20=13d)
=1+dd+23dd=23d1dd=132dd=13d2
=6×2132=40   [Using equation (1)]

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