awk — Sequences & Series

awk 'BEGIN{
    a1=5; d=3; n=10
    printf "a(n) = %d + (n-1)×%d\n", a1, d
    for(i=1;i<=n;i++) printf "a(%d) = %d\n", i, a1+(i-1)*d
}'

awk 'BEGIN{
    a1=1; d=2; n=100
    an=a1+(n-1)*d
    S=n*(a1+an)/2
    printf "sum of first %d odd numbers = %.0f\n", n, S
    printf "formula: n(a₁+aₙ)/2 = %d×(%d+%d)/2\n", n, a1, an
}'

awk 'BEGIN{
    a1=2; r=3; n=8
    printf "a(n) = %d × %d^(n-1)\n", a1, r
    for(i=1;i<=n;i++) printf "a(%d) = %.0f\n", i, a1*r^(i-1)
}'

awk 'BEGIN{
    a1=1; r=0.5; n=20
    # Finite sum: a₁(1-rⁿ)/(1-r)
    S_finite=a1*(1-r^n)/(1-r)
    # Infinite sum (|r|<1): a₁/(1-r)
    S_inf=a1/(1-r)
    printf "finite sum (n=%d): %.10f\n", n, S_finite
    printf "infinite sum:      %.10f\n", S_inf
    printf "difference:        %.10f\n", S_inf-S_finite
}'

awk 'BEGIN{
    sum=0
    for(n=1;n<=1000000;n++){
        sum+=1/n
        if(n==10||n==100||n==1000||n==10000||n==100000||n==1000000)
            printf "H(%7d) = %.6f\n", n, sum
    }
}'

awk 'BEGIN{
    a=0; b=1; n=20
    for(i=1;i<=n;i++){
        printf "F(%2d) = %d\n", i, b
        temp=a+b; a=b; b=temp
    }
}'

echo "27" | awk '{
    n=$1; steps=0
    printf "%d", n
    while(n!=1){
        n=(n%2==0)?n/2:3*n+1
        printf " → %d", n
        steps++
    }
    printf "\n(%d steps)\n", steps
}'

awk 'BEGIN{
    x=1   # compute e^1 = e
    sum=1; term=1
    for(n=1;n<=20;n++){
        term*=x/n
        sum+=term
        if(n<=5||n==10||n==15||n==20)
            printf "n=%2d: e^%.0f ≈ %.10f\n", n, x, sum
    }
    printf "actual: %.10f\n", exp(x)
}'

awk 'BEGIN{
    cost=50000; salvage=5000; life=5
    sl_dep=(cost-salvage)/life
    printf "%-6s %12s %12s %12s\n", "Year", "Straight", "Declining", "Book Value"
    bv_sl=cost; bv_db=cost
    rate=2.0/life   # double declining
    for(y=1;y<=life;y++){
        db_dep=bv_db*rate
        if(bv_db-db_dep<salvage) db_dep=bv_db-salvage
        bv_sl-=sl_dep; bv_db-=db_dep
        printf "%-6d %12.2f %12.2f %12.2f\n", y, sl_dep, db_dep, bv_db
    }
}'

cat <<'EOF' | awk '{uptime*=$1/100} BEGIN{uptime=1} END{
    printf "compound uptime: %.6f%%\n", uptime*100
    printf "annual downtime: %.2f minutes\n", (1-uptime)*525960
}'
99.95
99.90
99.99
99.95
99.85
99.99
99.95
99.90
99.99
99.95
99.99
99.90
EOF

awk 'BEGIN{
    start=1000; finish=2500; years=5
    cagr=exp(log(finish/start)/years)-1
    printf "CAGR: %.2f%%\n", cagr*100
    printf "\nProjection:\n"
    val=start
    for(y=0;y<=years;y++){
        printf "Year %d: $%.2f\n", y, val
        val*=(1+cagr)
    }
}'

awk 'BEGIN{
    printf "%5s %12s\n", "Disks", "Moves"
    for(n=1;n<=20;n++) printf "%5d %12.0f\n", n, 2^n-1
}'