Question

3. Find the sum of the following series upto n terms:
(i) 1 +5 + 11 + 19 +....​

Answer 1

Que:- (i) 1 +5 + 11 + 19 +....

Ans :- 1=1

5= 1+4

11=5+6

19 = 11+8

29= 19 + 10

.

.

.

The add all the equations and cancell the common terms to get

Tn = 1+{4+6+8+10+....to n terms}= 1+2{2+3+4+5+.... n terms} = 1+(n+2)(n-1) = n^2 + n -1

Now the reqd sum = n(n+1)(2n+1)/6 + n(n+1)/2 + n.

I assume that you know the summation formulae. If not revise those first!

Hope it helps

Answer 2

❤ hOlA mAtE ❤

==> Ans : - 1 = 1

==> 5 = 1 + 4

==> 11 = 5 + 6

==> 19 = 11 + 8 29 = 19 + 10

==> The add all the equations and cancell the common terms to get

==> Tn = 1+ { 4 + 6 + 8 + 10 + ... to n terms }

==> = 1 + 2 { 2 + 3 + 4 + 5 + .... n terms }

==>= 1+ ( n + 2 ) ( n - 1 ) = n ^ 2 + n - 1 Now the reqd sum = n ( n + 1 ) ( 2n + 1 ) / 6 + n ( n + 1 ) / 2 + n - 1 .

==>I assume that you know the

summation formulae . If not revise those first !