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JEE Main202524 Jan 2025Evening ShiftMathematicsSequences and SeriesActual

If 7=5+ 1 7 (5+ )+ 1 7^2 (5+2 )+ 1 7^3 (5+3 )+ , then the value of is :

Options

  1. A6 7
  2. B6
  3. C1 7
  4. D1

Correct answer

B. 6

Step-by-step solution

S=a+(a+d) r+(a+2 d) r^2+ Then S= a 1-r + d r (1-r)^2 ,|r| < 1 Since, r= 1 7 and a=5, d= aligned & 7= 5 1- 1 7 + 1 7 (1- 1 7 )^2 & =6 aligned

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