If An - (An-1) =1 for every positive integer greater than 1, then A1+ A2 + A3 - Maths - Sequences and Series

Question

If An - (An-1) =1 for every positive integer greater than 1, then
A1+ A2 + A3 +A100 =? Answer is 5050 A1

Rishabh Mittal · Accepted Answer

Dear Student ,
Please find below the solution to the asked query :

An-An-1=1For n=2 , A2-A2-1=1A2-A1=1For n =3A3-A2=1So , is is an AP with d=1 
A1+A2+A3+ +A100a=A1 , d=1 , n=100 
sn=n22a+n-1d=1002 2A1+100-11=50 2A1+99=100A1+4950   ANS
Please recheck answer posted by you 
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If An - (An-1) =1 for every positive integer greater than 1, then A1+ A2 + A3... +A100 =? Answer is 5050.A1