s1+s2+s3+s4...+sn > 9/10 ?mariah wrote:4. Sequence s1,s2,s3,..sn, is such that s=1/n-1/n+1 . Is the sum of first n terms greater than 9/10?
1). n>10
2). n<19
s = (1/n) - (1/n+1)
we can see that s1's second term will cancel with s2's second term
so in the summation, s1+s2+s3+s4...+sn only (1)-(1/n+1) will remain
1) n>10
when n = 11,
sum = 1 - (1/12) = 11/12 = 0.91>0.9
hence as n increases (1/n+1) decreases so 1-(1/n+1) increases
hence suff
2) when n = 1, sum = 0
when n = 11, sum >.9
insuff
Ans = A
