Verified Solution • 2025–26 Session moderate

QJEEM25Mac7d8: JEE Main 2025 Mathematics - Class 11 JEEM25Mac7d8 Solution: If , then the value of is :

If 7=5+17(5+α)+172(5+2α)+173(5+3α)+…………∞7=5+\frac{1}{7}(5+\alpha)+\frac{1}{7^2}(5+2 \alpha)+\frac{1}{7^3}(5+3 \alpha)+\ldots \ldots \ldots \ldots \infty , then the value of α\alpha is :

Multiple Choice Options

  • A 17\frac{1}{7}
  • B 1
  • C 67\frac{6}{7}
  • D 6

Step-by-Step Verified Solution

 Let S=5+17(5+α)+172(5+2α)+…17S=17(5)+172(5+α)+…∞

67(S)=5+17α(11−17)6=5+α6⇒α=6

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