Question

plz solve this questions....​

Answer 1

Step-by-step explanation:

Let the GP is a , ar , ar² , ar³ , .......... arⁿ⁻¹.

S = Sum of n terms

= a + ar + ar² + ar³ + .......+ arⁿ⁻¹

= a( rⁿ - 1)/( r - 1)

and R = sum of reciprocal of n terms

= 1/a + 1/ar + 1/ar² + 1/ar³ + ......... + 1/arⁿ⁻¹

= 1/a[ 1 - ( 1/r )ⁿ ]/( 1 - 1/r )

= ( rⁿ - 1)r/arⁿ(r - 1)

P = product of n terms = a × ar × ar² × ar³ × .....× arⁿ⁻¹

=〈 a¹⁺¹⁺¹⁺¹⁺¹⁺¹⁺¹⁺⁻⁻¹〉〈r¹⁺²⁺³⁺⁻⁻⁻⁻⁽ⁿ⁻¹⁾〉

= aⁿ. r^{n(n-1)/2}

take square both sides,

P² = a²ⁿrⁿ⁽ⁿ⁻¹⁾

Now, we have to prove P²Rⁿ = Sⁿ

or , P² = (S/R)ⁿ

RHS = (S/R)ⁿ

= [a(rⁿ - 1)/(r - 1) ]/[(rⁿ - 1)r/arⁿ(r - 1) ]ⁿ

= [a(rⁿ - 1)/(r - 1) × arⁿ (r - 1)/(rⁿ - 1)r ]ⁿ

=〈 a²rⁿ⁻¹ 〉ⁿ

= a²ⁿ rⁿ⁽ⁿ⁻¹⁾ = P² = LHS

Answer 2

Answer:

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