0

Guest

Courses New

The value of 1+1/4+1/16+1/64.....upto infinity is (a)5/4 (b)4/3 (c)6/5 (d)7/6

The value of 1+1/4+1/16+1/64.....upto infinity is (a)5/4 (b)4/3 (c)6/5 (d)7/6

Grade:11

2 Answers

Harsh Vardhan
12 Points
6 years ago
1+1/4+1/16......infinity=1/2^0 +1/2^2 +1/2^4..........1/2^n=(2^n + 2^(n-2) + 2^(n-4) ......2^0) /2^n [Simlple lcm and add]If u hv noticed numinator forms a gpTherefore r = a2/a1 = 2(n-2)/2^n = 1/4Apply infinite gp add formula A1/1-r = 2^n/1-1/4= 2^n/(3/4) = (4x2^n)/3 {this is numinator}Now put the dinominator as it is= ((4 x 2^n)/3)/2^n= 4/3 (b).So b option is correctI hv learned gp half an hour ago....while trying this😅.
Prerna
15 Points
3 years ago
1+1/4+1/16+1/64.................since it is GP and the formula for the sum of infinite GP is
a/1-r
here a=1 and r=1/4
=1/1-1/4
=4/3

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More