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The sum of the series: 1+ 1 1+2 + 1 1+2+3 + . upto 10 terms, is:

Options

  1. A18 11
  2. B22 13
  3. C20 11
  4. D16 9

Correct answer

C. 20 11

Step-by-step solution

T _r= 1 1+2+3+ +r = 2 r(r+1) S ₁₀=2 _ r=1 ¹⁰ 1 r(r+1) =2 _ r=1 ¹⁰ [ r+1 r(r+1) - r r(r+1) ]=2 _ r=1 ¹⁰ ( 1 r - 1 r+1 )=2 [ ( 1 1 - 1 2 )+ ( 1 2 - 1 3 )+ ( 1 3 - 1 4 )+ + ( 1 10 - 1 11 ) ]=2 [1- 1 11 ]=2 10 11 = 20 11

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