The value of displaystyle∑n=1∞ (5n-2n/10n) is equal to

Question

The value of displaystyle∑n=1∞ (5n-2n/10n) is equal to (A) 1 (B) (1/4) (C) (1/3) (D) (3/4)

Tardigrade Admin · Accepted Answer

displaystyle∑n=1∞ (5n-2n/10n)= displaystyle∑n=1∞((5n/10n)-(2n/10n))= displaystyle∑n=1∞((1/2))n-((1/5))n the difference between two infinite geometric sequences =((1/2)/1-(1)2)-((1/5)/1-(1)5)=1-(1/4)=(3/4)

Q. The value of $n = 1 \sum \infty \frac{5 ^{n} - 2 ^{n}}{1 0 ^{n}}$ is equal to

1

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{3}{4}$

Q. The value of n=1∑∞​10n5n−2n​ is equal to

1

41​

31​

43​

n=1∑∞​10n5n−2n​=n=1∑∞​(10n5n​−10n2n​)=n=1∑∞​(21​)n−(51​)n the difference between two infinite geometric sequences =1−21​21​​−1−51​51​​=1−41​=43​

Q. The value of $n = 1 \sum \infty \frac{5 ^{n} - 2 ^{n}}{1 0 ^{n}}$ is equal to

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{3}{4}$