solve 19 question in full solution
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Hi ,
m th term = tm = 2^m + 2m
n th term = 2^n + 2n
Sum of n terms = Sn
Sn = sigma ( 2^n + 2m ) ---( 1 )
i ) sigma 2^n = 2+2²+2³ + ....+ 2^n
is in G.P
First term = a = 2
Common ratio = r = 2
Sn = [ a ( r^n - 1 ) ] / ( r - 1 )
= [ 2 ( 2^n - 1 ) ] / ( 2 - 1 )
= 2( 2^n - 1 ) ----( 2 )
ii ) sigma 2n = 2 × sigma n
= [ 2 n ( n + 1 ) / 2 ]
= n ( n + 1 ) ---- ( 3 )
Therefore ,
Sn = ( 2 ) + ( 3 )
= 2 ( 2^n - 1 ) + n² + n
I hope this helps you.
:)
m th term = tm = 2^m + 2m
n th term = 2^n + 2n
Sum of n terms = Sn
Sn = sigma ( 2^n + 2m ) ---( 1 )
i ) sigma 2^n = 2+2²+2³ + ....+ 2^n
is in G.P
First term = a = 2
Common ratio = r = 2
Sn = [ a ( r^n - 1 ) ] / ( r - 1 )
= [ 2 ( 2^n - 1 ) ] / ( 2 - 1 )
= 2( 2^n - 1 ) ----( 2 )
ii ) sigma 2n = 2 × sigma n
= [ 2 n ( n + 1 ) / 2 ]
= n ( n + 1 ) ---- ( 3 )
Therefore ,
Sn = ( 2 ) + ( 3 )
= 2 ( 2^n - 1 ) + n² + n
I hope this helps you.
:)
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