Question

Find the flowing series.
(iii) 51+52 +53+...+92
(iv) + 4+9+16 tarot 225
(v) 6²+72+82 +...+212
(vi) 103+113 +123+..
+203
%
(vii) 1+3+5+...+71
1) 51 +52 +53 +...+92​

Answer 1

51 +52+53+_________92
= (1+2+3+________+92 ) -(1+2+_____+50)
Use 1+2+3_______+n = n(n+1)/2
92*93/2-50*51/2
4278-1275 = 3003


1+4+9________225
Use sum up to n^2 = n(n+1)(2n+1)/6
Here n= 15
So S = 15*16*31/6 = 1240


(V) 6^2+7^2+______+21^2
= (1^2+2^2+————-21^2)-(1^2+2^2+——+5^2)
21(22)(43)/6- 5(6)(11)/6
3311-55= 3256

Use sum of cubes = { n(n+1)/2}^2