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Grade: 12
        
Let x1x x2x x3,........ Are In HP then value of summation k=1to k=20 (-1)^k.(xk+xk+1/xk-xk+1) equals to
one year ago

Answers : (1)

Pavan Kumar
32 Points
							
Hi , thank you for asking the question      
consider  (-1)k(xk+xk+1/xk  - x k+1)     ~1
now ,as they are in H.P their inverse is in A.P and let common difference is r
1/xk+1=1/xk+r
1/xk+1 – 1/xk =r
1/( xk    –  xk+1  )=1/(r* xk  *xk+1)   ~2
substitute 2 in 1 then we get
(-1)k(xk+xk+1/r* xk  *xk+1)=  (-1)k(1/r)(1/ xk  +1/ xk+1 )
so the sequence we come as    -1(1/r)(1/x1+1/x2)+1/r(1/x2+1/x3)............
(1/r)[-1/x1+1/x21]=     (1/r)[1/x21-1/x1]
Hope you got the solution .if there is any problem in understanding the solution continue the thread.                        
one year ago
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