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				   Obtain the nth term and sum of the following terms upto n terms
(a) Sn = 1.2.3 + 3.4.5 + 5.6.7 + 7.8.9+.........
(b) Sn = 1.2.3.4 + 2.3.4.5 + 3.4.5.6 + ............


7 years ago

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										1+2+3+4+...........+n      =  n2/2 + n/2
12+22+32+ ....... +n2     = n3/3 + n2/2 + n/6
13+23+33+ ....... +n3     = n4/4 + n3/2 + n2/4
14+24+34+ ....... +n4     = n5/5 + n4/2 + n3/3 - n/30
a) Sn = 1.2.3 + 3.4.5 + 5.6.7 + 7.8.9+.........
n is set of natural no's 1,2,3.......n
n th term is (2n-1).(2n).(2n+1)
sum of n terms
= 8( sigma: n3 ) - 2( sigma : n )
= 8.n2(n+1)2/4 -n(n+1)
= n(n+1).(2n2+2n-1)
b) Sn = 1.2.3.4 + 2.3.4.5 + 3.4.5.6 + ............
n is set of natural no's 1,2,3.......n
n th term is: n(n+1)(n+2)(n+3)
= n4 + 6n3+ 11n2 + 6n
sum of n terms
= ( sigma: n4 ) + 6( sigma : n3 ) + 11.( sigma: n2 ) + 6( sigma : n )
=  (n5/5 + n4/2 + n3/3 - n/30) +6(n4/4 + n3/2 + n2/4)+11(n3/3 + n2/2 + n/6)+6(n2/2 + n/2)
=  n5/5 + 2.n4 + 7.n3 +10. n2+  9n/2
--
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we will get you the answer and detailed solution very quickly.We are all IITians and here to help you in your IIT JEE preparation. All the best.

Regards,
Naga Ramesh
IIT Kgp - 2005 batch

7 years ago

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