Question

Find the sum of n terms of series the rth term of which is (2r+1)2^r

Answer 1

Hi ,

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For an A.G.P ,

Sum of r terms = a/( 1 - r ) + rd/(1-r)²

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Tr = ( 2r + 1 )2^r

T1 = ( 2 × 1 + 1 ) 2^1 = 3 × 2

Similarly ,

T2 = 5 × 2²

T3 = 7 × 2³

:
:
Tn = ( 2n + 1 )2ⁿ

Here ,

a = 3 , d = 2 , r = 2

Sum of n terms

= 3/( 1 - 2 ) + ( 2 × 2 )/( 1 - 2 )²

= 3/( -1 ) + 4/( - 1 )²

= -3 + 4

= 1

I hope this helps you.

: )

Answer 2

Answer

Sum of r terms = a / ( 1 - r ) + rd / ( 1 - r )2

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Tr = (2r+1) 2^r

T1 = (2×1+1) 2^1=3×2

Similarly,

T2 =5×2

T3 =7×2

:

:

Tn =(2n+1) 2n

Here

a= 3,d=2,r=2

Sum of n terms

= 3/(1-2)+(2×2)/(1-2)2

= 3/(-1 ) +4/(-1 )2

= -3+4

=1