Question

the numbers of terms to be taken so that 1+2+4+8+ will be 8191 is

Answer 1

So it will help you to get the answer

Answer 2

Value of n = 13

From the series of the given GP, we get

a=1 , r=2

we know that,

Sum of a series is  

Sₙ = a(rⁿ -1) / r-1

Solving for the value of n

⇒ 8191 = 1 (2ⁿ -1)/2-1

⇒ 8191 + 1 = 2ⁿ

⇒ 8192 = 2ⁿ

⇒ 2¹³ = 2ⁿ

As, the base values are equal, the powers are also equal.

⇒  n = 13

Therefore, number of terms to be taken so that 1+2+4+8+.... will be 8191 is 13

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