The sum of the first m terms of an arithmetic series is n and the first n terms is
m. Find the sum of first (m+n) terms.
1 8. If the pth,qth and rth terms of an arithmetic series are a,b,c, respectively,
show that a(qr)b(rp)c(pq) 0.
Show that, 1 3 5 7 125 196 171 713 209.
A man agrees to refund the loan of Tk. 20 0 0 in some parts. Each part is Tk. 2
more than the previous part. If the first part is Tk. 1, in how many parts will the
man be able to refund that amount?
Determinaton of the sum of Squares of the first n numbers of Natural Numbers
Let Sn be the number of squares of the first n numbers of natural numbers
i.e.,Sn 12 22 32 n^2
We know,
r^3 3 r^2 3 r 1 (r 1 )^3
or, r^3 (r 1 )^3 3 r^2 3 r 1
In the above identity, putting, r 1 , 2 , 3 ,,n we get,
( 1 ) 3. 3. 13 2 3. 3 3. 3 12 1 3. 2 3. 2 11 0 3. 1 3. 1 13 3 23 3 23 3 23 3 2 n n n n Adding, we get,
n^3 03 3 ( 12 22 32 n^2 ) 3 ( 1 2 3 n)( 1 1 1 1 )
or, »
¼
º
«
»
2( 1 )
1 2 3
2( 1 )(^333).
nn
n n
nn
n Sn
or, n
nn
Sn n
2
3 ( 1 )
3 3
2
{ 2 ( 1 ) 1 ( 1 )}
2
( 2
2 2
2
2
2
2 1 )
3 3 2 3 ( 2 3 1 )
2
3 2 3 2 2
n n n nn n
n n n
n n
n n n n n n n
or,
2
( 1 )( 2 1 )
3
nn n
Sn
?
6
( 1 )( 2 1 )
nn n
Sn