The greatest value of n so that 1 + 5 + 52 + 53 + …………. n te

1.	The greatest value of n so that 1 + 5 + 52 + 53 + …………. n terms is less than 4321 is ……………….. A) 7 B) 6 C) 9 D) 8
Answer» Correct option is (B) 6 Let \(1 + 5 + 5^2 + 5^3 +.......+n\) terms < 4321 \(\Rightarrow\frac{1(5^n-1)}{5-1}<4321\) \(\Rightarrow5^n-1<4321\times4\) \(\Rightarrow5^n-1<17284\) \(\Rightarrow5^n<17285\) \(\because5^6=15625<17285\) But \(5^7=78125>17285\) Hence, greatest value of n is 6 so that the sum \(1+5+5^2+5^3+.......\) is less than 4321. Correct option is B) 6

The greatest value of n so that 1 + 5 + 52 + 53 + …………. n terms is less than 4321 is ……………….. A) 7 B) 6 C) 9 D) 8

Answer»

Correct option is (B) 6

Let \(1 + 5 + 5^2 + 5^3 +.......+n\) terms < 4321

\(\Rightarrow\frac{1(5^n-1)}{5-1}<4321\)

\(\Rightarrow5^n-1<4321\times4\)

\(\Rightarrow5^n-1<17284\)

\(\Rightarrow5^n<17285\)

\(\because5^6=15625<17285\)

But \(5^7=78125>17285\)

Hence, greatest value of n is 6 so that the sum \(1+5+5^2+5^3+.......\) is less than 4321.

Correct option is B) 6