If (10)⁹ + 2(11)(10)⁸ + 3(11)²(10)⁷ + ... + 10(11)⁹ = k(10)⁹, then k is equal to

Let the sum be denoted by S thenS=109+2×11×108+3×112×107+.+10×119or,1110S=11×108+2×112×107+.+9×119+11×119on subtracting we getS10=109+11×108+112×107+..+118×10+119�we can see that except the last term all the terms are in G.P with a =109and r=1110Hence⇒S10=109(111010𕒵)1110𕒵�=1010(111010𕒵)�⇒S=10×1010=100(10)9Therefore,k=100