Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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

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 + ............

Grade:12

1 Answers

Ramesh V
70 Points
11 years ago

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

--

Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and
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

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free