SOLUTION: 1995/1×2 +1995/2×3 + 1995/3×4 +.....+1995/1994×1995

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Question 964587: 1995/1×2 +1995/2×3 + 1995/3×4 +.....+1995/1994×1995
Answer by amarjeeth123(569) About Me  (Show Source):
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1995/1×2 +1995/2×3 + 1995/3×4 +.....+1995/1994×1995
The given series is equal toΣ 1995(1/(n-1)n)
=1995Σ((1/n-1)-(1/n))
=1995(1-1/2+1/2-1/3+1/3-1/4+.......+1/1993-1/1994+1/1994-1/1995)
=1995(1-1/1995)
=1995(1994/1995)
=1994.
Answer=1994.