Find k in JEE Mains Homework: Solving Equations with Geometric Progressions

[smart_worker]

Homework Statement

Find k.

Homework Equations

If (10)⁹ + 2(11)¹ (10)⁸ + 3(11)² (10)⁷ + ...… + 10 (11)⁹ = k(10)⁹

The Attempt at a Solution

dividing both sides by 10⁹,

1 + {2(11)¹}/(10)¹} + {3(11)²}/(10)²} + ..... + {10(11)⁹}/(10)⁹} = k

1(1.1)⁰ + 2(1.1)¹ + 3(1.1)² + ... + 10(1.1)⁹

∑(from n=0 to n=9) (n+1)(1.1)ⁿ

 

[AGNuke]

It's an AGP. What's the problem?

 

[xiavatar]

http://en.wikipedia.org/wiki/Arithmetico-geometric_sequence